Question
Which graphs represents the correct translation of right triangle DEF
on the coordinate plane with the following rule (x+3,y+1)
?(1 point)
Responses
1.A coordinate plane shows all four quadrants with both axes ranging from negative 8 to 8 in increments of 1. Two right triangles are graphed on the plane. Three points labeled as upper D, upper E, and upper F are plotted at coordinates left parenthesis negative 6 comma negative 5 right parenthesis, left parenthesis negative 6 comma negative 2 right parenthesis, and left parenthesis negative 3 comma negative 5 right parenthesis, respectively. The three points are joined by solid lines to form triangle upper D upper E upper F whose base is upper D upper F, hypotenuse is upper E upper F, and perpendicular side is upper D upper E. Three other points labeled as upper D prime, upper E prime, and upper F prime are plotted at coordinates left parenthesis negative 5 comma negative 2 right parenthesis, left parenthesis negative 5 comma 1 right parenthesis, and left parenthesis negative 2 comma negative 2 right parenthesis, respectively. These three points are joined by dotted lines to form triangle upper D prime upper E prime upper F prime whose base is upper D prime upper F prime, hypotenuse is upper E prime upper F prime, and perpendicular side is upper D prime upper E prime.
Image with alt text: A coordinate plane shows all four quadrants with both axes ranging from negative 8 to 8 in increments of 1. Two right triangles are graphed on the plane. Three points labeled as upper D, upper E, and upper F are plotted at coordinates left parenthesis negative 6 comma negative 5 right parenthesis, left parenthesis negative 6 comma negative 2 right parenthesis, and left parenthesis negative 3 comma negative 5 right parenthesis, respectively. The three points are joined by solid lines to form triangle upper D upper E upper F whose base is upper D upper F, hypotenuse is upper E upper F, and perpendicular side is upper D upper E. Three other points labeled as upper D prime, upper E prime, and upper F prime are plotted at coordinates left parenthesis negative 5 comma negative 2 right parenthesis, left parenthesis negative 5 comma 1 right parenthesis, and left parenthesis negative 2 comma negative 2 right parenthesis, respectively. These three points are joined by dotted lines to form triangle upper D prime upper E prime upper F prime whose base is upper D prime upper F prime, hypotenuse is upper E prime upper F prime, and perpendicular side is upper D prime upper E prime.
2.A coordinate plane shows all four quadrants with both axes ranging from negative 8 to 8 in increments of 1. Two right triangles are graphed on the plane. Three points labeled as upper D, upper E, and upper F are plotted at coordinates left parenthesis negative 3 comma negative 4 right parenthesis, left parenthesis negative 3 comma negative 1 right parenthesis, and left parenthesis 0 comma negative 4 right parenthesis, respectively. The three points are joined by solid lines to form triangle upper D upper E upper F whose base is upper D upper F, hypotenuse is upper E upper F, and perpendicular side is upper D upper E. Three other points labeled as upper D prime, upper E prime, and upper F prime are plotted at coordinates left parenthesis negative 6 comma negative 5 right parenthesis, left parenthesis negative 6 comma negative 2 right parenthesis, and left parenthesis negative 3 comma negative 5 right parenthesis, respectively. These three points are joined by dotted lines to form triangle upper D prime upper E prime upper F prime whose base is upper D prime upper F prime, hypotenuse is upper E prime upper F prime, and perpendicular side is upper D prime upper E prime.
Image with alt text: A coordinate plane shows all four quadrants with both axes ranging from negative 8 to 8 in increments of 1. Two right triangles are graphed on the plane. Three points labeled as upper D, upper E, and upper F are plotted at coordinates left parenthesis negative 3 comma negative 4 right parenthesis, left parenthesis negative 3 comma negative 1 right parenthesis, and left parenthesis 0 comma negative 4 right parenthesis, respectively. The three points are joined by solid lines to form triangle upper D upper E upper F whose base is upper D upper F, hypotenuse is upper E upper F, and perpendicular side is upper D upper E. Three other points labeled as upper D prime, upper E prime, and upper F prime are plotted at coordinates left parenthesis negative 6 comma negative 5 right parenthesis, left parenthesis negative 6 comma negative 2 right parenthesis, and left parenthesis negative 3 comma negative 5 right parenthesis, respectively. These three points are joined by dotted lines to form triangle upper D prime upper E prime upper F prime whose base is upper D prime upper F prime, hypotenuse is upper E prime upper F prime, and perpendicular side is upper D prime upper E prime.
3.A coordinate plane shows all four quadrants with both axes ranging from negative 8 to 8 in increments of 1. Two right triangles are graphed on the plane. Three points labeled as upper D, upper E, and upper F are plotted at coordinates left parenthesis negative 6 comma negative 5 right parenthesis, left parenthesis negative 6 comma negative 2 right parenthesis, and left parenthesis negative 3 comma negative 5 right parenthesis, respectively. The three points are joined by solid lines to form triangle upper D upper E upper F whose base is upper D upper F, hypotenuse is upper E upper F, and perpendicular side is upper D upper E. Three other points labeled as upper D prime, upper E prime, and upper F prime are plotted at coordinates left parenthesis negative 3 comma negative 4 right parenthesis, left parenthesis negative 3 comma negative 1 right parenthesis, and left parenthesis 0 comma negative 4 right parenthesis, respectively. These three points are joined by dotted lines to form triangle upper D prime upper E prime upper F prime whose base is upper D prime upper F prime, hypotenuse is upper E prime upper F prime, and perpendicular side is upper D prime upper E prime.
Image with alt text: A coordinate plane shows all four quadrants with both axes ranging from negative 8 to 8 in increments of 1. Two right triangles are graphed on the plane. Three points labeled as upper D, upper E, and upper F are plotted at coordinates left parenthesis negative 6 comma negative 5 right parenthesis, left parenthesis negative 6 comma negative 2 right parenthesis, and left parenthesis negative 3 comma negative 5 right parenthesis, respectively. The three points are joined by solid lines to form triangle upper D upper E upper F whose base is upper D upper F, hypotenuse is upper E upper F, and perpendicular side is upper D upper E. Three other points labeled as upper D prime, upper E prime, and upper F prime are plotted at coordinates left parenthesis negative 3 comma negative 4 right parenthesis, left parenthesis negative 3 comma negative 1 right parenthesis, and left parenthesis 0 comma negative 4 right parenthesis, respectively. These three points are joined by dotted lines to form triangle upper D prime upper E prime upper F prime whose base is upper D prime upper F prime, hypotenuse is upper E prime upper F prime, and perpendicular side is upper D prime upper E prime.
4.A coordinate plane shows all four quadrants with both axes ranging from negative 8 to 8 in increments of 1. Two overlapping right triangles are graphed on the plane. Three points labeled as upper D, upper E, and upper F are plotted at coordinates left parenthesis negative 6 comma negative 5 right parenthesis, left parenthesis negative 6 comma negative 2 right parenthesis, and left parenthesis negative 3 comma negative 5 right parenthesis, respectively. The three points are joined by solid lines to form triangle upper D upper E upper F whose base is upper D upper F, hypotenuse is upper E upper F, and perpendicular side is upper D upper E. Three other points labeled as upper D prime, upper E prime, and upper F prime are plotted at coordinates left parenthesis negative 3 comma negative 5 right parenthesis, left parenthesis negative 3 comma negative 2 right parenthesis, and left parenthesis 0 comma negative 5 right parenthesis, respectively. These three points are joined by dotted lines to form triangle upper D prime upper E prime upper F prime whose base is upper D prime upper F prime, hypotenuse is upper E prime upper F prime, and perpendicular side is upper D prime upper E prime. The two triangles intersect at points upper F and upper D prime.
Image with alt text: A coordinate plane shows all four quadrants with both axes ranging from negative 8 to 8 in increments of 1. Two overlapping right triangles are graphed on the plane. Three points labeled as upper D, upper E, and upper F are plotted at coordinates left parenthesis negative 6 comma negative 5 right parenthesis, left parenthesis negative 6 comma negative 2 right parenthesis, and left parenthesis negative 3 comma negative 5 right parenthesis, respectively. The three points are joined by solid lines to form triangle upper D upper E upper F whose base is upper D upper F, hypotenuse is upper E upper F, and perpendicular side is upper D upper E. Three other points labeled as upper D prime, upper E prime, and upper F prime are plotted at coordinates left parenthesis negative 3 comma negative 5 right parenthesis, left parenthesis negative 3 comma negative 2 right parenthesis, and left parenthesis 0 comma negative 5 right parenthesis, respectively. These three points are joined by dotted lines to form triangle upper D prime upper E prime upper F prime whose base is upper D prime upper F prime, hypotenuse is upper E prime upper F prime, and perpendicular side is upper D prime upper E prime. The two triangles intersect at points upper F and upper D prime.
Skip to navigation
on the coordinate plane with the following rule (x+3,y+1)
?(1 point)
Responses
1.A coordinate plane shows all four quadrants with both axes ranging from negative 8 to 8 in increments of 1. Two right triangles are graphed on the plane. Three points labeled as upper D, upper E, and upper F are plotted at coordinates left parenthesis negative 6 comma negative 5 right parenthesis, left parenthesis negative 6 comma negative 2 right parenthesis, and left parenthesis negative 3 comma negative 5 right parenthesis, respectively. The three points are joined by solid lines to form triangle upper D upper E upper F whose base is upper D upper F, hypotenuse is upper E upper F, and perpendicular side is upper D upper E. Three other points labeled as upper D prime, upper E prime, and upper F prime are plotted at coordinates left parenthesis negative 5 comma negative 2 right parenthesis, left parenthesis negative 5 comma 1 right parenthesis, and left parenthesis negative 2 comma negative 2 right parenthesis, respectively. These three points are joined by dotted lines to form triangle upper D prime upper E prime upper F prime whose base is upper D prime upper F prime, hypotenuse is upper E prime upper F prime, and perpendicular side is upper D prime upper E prime.
Image with alt text: A coordinate plane shows all four quadrants with both axes ranging from negative 8 to 8 in increments of 1. Two right triangles are graphed on the plane. Three points labeled as upper D, upper E, and upper F are plotted at coordinates left parenthesis negative 6 comma negative 5 right parenthesis, left parenthesis negative 6 comma negative 2 right parenthesis, and left parenthesis negative 3 comma negative 5 right parenthesis, respectively. The three points are joined by solid lines to form triangle upper D upper E upper F whose base is upper D upper F, hypotenuse is upper E upper F, and perpendicular side is upper D upper E. Three other points labeled as upper D prime, upper E prime, and upper F prime are plotted at coordinates left parenthesis negative 5 comma negative 2 right parenthesis, left parenthesis negative 5 comma 1 right parenthesis, and left parenthesis negative 2 comma negative 2 right parenthesis, respectively. These three points are joined by dotted lines to form triangle upper D prime upper E prime upper F prime whose base is upper D prime upper F prime, hypotenuse is upper E prime upper F prime, and perpendicular side is upper D prime upper E prime.
2.A coordinate plane shows all four quadrants with both axes ranging from negative 8 to 8 in increments of 1. Two right triangles are graphed on the plane. Three points labeled as upper D, upper E, and upper F are plotted at coordinates left parenthesis negative 3 comma negative 4 right parenthesis, left parenthesis negative 3 comma negative 1 right parenthesis, and left parenthesis 0 comma negative 4 right parenthesis, respectively. The three points are joined by solid lines to form triangle upper D upper E upper F whose base is upper D upper F, hypotenuse is upper E upper F, and perpendicular side is upper D upper E. Three other points labeled as upper D prime, upper E prime, and upper F prime are plotted at coordinates left parenthesis negative 6 comma negative 5 right parenthesis, left parenthesis negative 6 comma negative 2 right parenthesis, and left parenthesis negative 3 comma negative 5 right parenthesis, respectively. These three points are joined by dotted lines to form triangle upper D prime upper E prime upper F prime whose base is upper D prime upper F prime, hypotenuse is upper E prime upper F prime, and perpendicular side is upper D prime upper E prime.
Image with alt text: A coordinate plane shows all four quadrants with both axes ranging from negative 8 to 8 in increments of 1. Two right triangles are graphed on the plane. Three points labeled as upper D, upper E, and upper F are plotted at coordinates left parenthesis negative 3 comma negative 4 right parenthesis, left parenthesis negative 3 comma negative 1 right parenthesis, and left parenthesis 0 comma negative 4 right parenthesis, respectively. The three points are joined by solid lines to form triangle upper D upper E upper F whose base is upper D upper F, hypotenuse is upper E upper F, and perpendicular side is upper D upper E. Three other points labeled as upper D prime, upper E prime, and upper F prime are plotted at coordinates left parenthesis negative 6 comma negative 5 right parenthesis, left parenthesis negative 6 comma negative 2 right parenthesis, and left parenthesis negative 3 comma negative 5 right parenthesis, respectively. These three points are joined by dotted lines to form triangle upper D prime upper E prime upper F prime whose base is upper D prime upper F prime, hypotenuse is upper E prime upper F prime, and perpendicular side is upper D prime upper E prime.
3.A coordinate plane shows all four quadrants with both axes ranging from negative 8 to 8 in increments of 1. Two right triangles are graphed on the plane. Three points labeled as upper D, upper E, and upper F are plotted at coordinates left parenthesis negative 6 comma negative 5 right parenthesis, left parenthesis negative 6 comma negative 2 right parenthesis, and left parenthesis negative 3 comma negative 5 right parenthesis, respectively. The three points are joined by solid lines to form triangle upper D upper E upper F whose base is upper D upper F, hypotenuse is upper E upper F, and perpendicular side is upper D upper E. Three other points labeled as upper D prime, upper E prime, and upper F prime are plotted at coordinates left parenthesis negative 3 comma negative 4 right parenthesis, left parenthesis negative 3 comma negative 1 right parenthesis, and left parenthesis 0 comma negative 4 right parenthesis, respectively. These three points are joined by dotted lines to form triangle upper D prime upper E prime upper F prime whose base is upper D prime upper F prime, hypotenuse is upper E prime upper F prime, and perpendicular side is upper D prime upper E prime.
Image with alt text: A coordinate plane shows all four quadrants with both axes ranging from negative 8 to 8 in increments of 1. Two right triangles are graphed on the plane. Three points labeled as upper D, upper E, and upper F are plotted at coordinates left parenthesis negative 6 comma negative 5 right parenthesis, left parenthesis negative 6 comma negative 2 right parenthesis, and left parenthesis negative 3 comma negative 5 right parenthesis, respectively. The three points are joined by solid lines to form triangle upper D upper E upper F whose base is upper D upper F, hypotenuse is upper E upper F, and perpendicular side is upper D upper E. Three other points labeled as upper D prime, upper E prime, and upper F prime are plotted at coordinates left parenthesis negative 3 comma negative 4 right parenthesis, left parenthesis negative 3 comma negative 1 right parenthesis, and left parenthesis 0 comma negative 4 right parenthesis, respectively. These three points are joined by dotted lines to form triangle upper D prime upper E prime upper F prime whose base is upper D prime upper F prime, hypotenuse is upper E prime upper F prime, and perpendicular side is upper D prime upper E prime.
4.A coordinate plane shows all four quadrants with both axes ranging from negative 8 to 8 in increments of 1. Two overlapping right triangles are graphed on the plane. Three points labeled as upper D, upper E, and upper F are plotted at coordinates left parenthesis negative 6 comma negative 5 right parenthesis, left parenthesis negative 6 comma negative 2 right parenthesis, and left parenthesis negative 3 comma negative 5 right parenthesis, respectively. The three points are joined by solid lines to form triangle upper D upper E upper F whose base is upper D upper F, hypotenuse is upper E upper F, and perpendicular side is upper D upper E. Three other points labeled as upper D prime, upper E prime, and upper F prime are plotted at coordinates left parenthesis negative 3 comma negative 5 right parenthesis, left parenthesis negative 3 comma negative 2 right parenthesis, and left parenthesis 0 comma negative 5 right parenthesis, respectively. These three points are joined by dotted lines to form triangle upper D prime upper E prime upper F prime whose base is upper D prime upper F prime, hypotenuse is upper E prime upper F prime, and perpendicular side is upper D prime upper E prime. The two triangles intersect at points upper F and upper D prime.
Image with alt text: A coordinate plane shows all four quadrants with both axes ranging from negative 8 to 8 in increments of 1. Two overlapping right triangles are graphed on the plane. Three points labeled as upper D, upper E, and upper F are plotted at coordinates left parenthesis negative 6 comma negative 5 right parenthesis, left parenthesis negative 6 comma negative 2 right parenthesis, and left parenthesis negative 3 comma negative 5 right parenthesis, respectively. The three points are joined by solid lines to form triangle upper D upper E upper F whose base is upper D upper F, hypotenuse is upper E upper F, and perpendicular side is upper D upper E. Three other points labeled as upper D prime, upper E prime, and upper F prime are plotted at coordinates left parenthesis negative 3 comma negative 5 right parenthesis, left parenthesis negative 3 comma negative 2 right parenthesis, and left parenthesis 0 comma negative 5 right parenthesis, respectively. These three points are joined by dotted lines to form triangle upper D prime upper E prime upper F prime whose base is upper D prime upper F prime, hypotenuse is upper E prime upper F prime, and perpendicular side is upper D prime upper E prime. The two triangles intersect at points upper F and upper D prime.
Skip to navigation
Answers
GPT-4o mini
To apply the translation rule \((x + 3, y + 1)\) to the triangle DEF, we need to translate each of the points D, E, and F according to the given rule.
Given the original coordinates:
- \(D(-6, -5)\)
- \(E(-6, -2)\)
- \(F(-3, -5)\)
Now we apply the translation:
1. For point \(D(-6, -5)\):
\[
D' = (-6 + 3, -5 + 1) = (-3, -4)
\]
2. For point \(E(-6, -2)\):
\[
E' = (-6 + 3, -2 + 1) = (-3, -1)
\]
3. For point \(F(-3, -5)\):
\[
F' = (-3 + 3, -5 + 1) = (0, -4)
\]
So after the translation, the new coordinates are:
- \(D'(-3, -4)\)
- \(E'(-3, -1)\)
- \(F'(0, -4)\)
Now we need to identify which of the options matches these new coordinates.
Reviewing the responses:
1. **Response 1**: Coordinates of \(D', E', F'\) are not correct.
2. **Response 2**: Matches \(D', E', F'\) coordinates.
3. **Response 3**: Coordinates of \(D', E', F'\) are not correct.
4. **Response 4**: Coordinates of \(D', E', F'\) are not correct.
Thus, the correct representation of the translated triangle, according to the coordinates we calculated, is found in **Response 2**.
Given the original coordinates:
- \(D(-6, -5)\)
- \(E(-6, -2)\)
- \(F(-3, -5)\)
Now we apply the translation:
1. For point \(D(-6, -5)\):
\[
D' = (-6 + 3, -5 + 1) = (-3, -4)
\]
2. For point \(E(-6, -2)\):
\[
E' = (-6 + 3, -2 + 1) = (-3, -1)
\]
3. For point \(F(-3, -5)\):
\[
F' = (-3 + 3, -5 + 1) = (0, -4)
\]
So after the translation, the new coordinates are:
- \(D'(-3, -4)\)
- \(E'(-3, -1)\)
- \(F'(0, -4)\)
Now we need to identify which of the options matches these new coordinates.
Reviewing the responses:
1. **Response 1**: Coordinates of \(D', E', F'\) are not correct.
2. **Response 2**: Matches \(D', E', F'\) coordinates.
3. **Response 3**: Coordinates of \(D', E', F'\) are not correct.
4. **Response 4**: Coordinates of \(D', E', F'\) are not correct.
Thus, the correct representation of the translated triangle, according to the coordinates we calculated, is found in **Response 2**.