To find the new coordinates of a point after a translation, we need to add the same amount to the x-coordinate and the y-coordinate. In this case, since the line is translated up 3 units and to the right 2 units, we will add 2 to the x-coordinate and 3 to the y-coordinate.
For the point (1,-5), adding 2 to the x-coordinate gives us 1+2 = 3, and adding 3 to the y-coordinate gives us -5+3 = -2. So the new coordinates for this point are (3,-2).
For the point (4,-4), adding 2 to the x-coordinate gives us 4+2 = 6, and adding 3 to the y-coordinate gives us -4+3 = -1. So the new coordinates for this point are (6,-1).
Therefore, the correct answer is A. (3,-2) and (6,-1).
Michele translated a line up 3 units and to the right 2 units. If two points on the original line are (1,-5) and (4,-4), what are these two points following the translation?
A. (3,-2) and (6, -1)
B. (4,-2) and (6,-2)
C. (4,-3) and (7,-2)
D. (1,5) and (4,4)
11 answers
A line containing the points (-2,3) and (2,3) is reflected across the x-axis. How long is the reflected line?
A. not enough information
B. 3 units
C. infinitely long
D. 4 units
A. not enough information
B. 3 units
C. infinitely long
D. 4 units
When a line is reflected across the x-axis, the y-coordinates of the points on the line change sign, while the x-coordinates remain the same.
The original line contains the points (-2,3) and (2,3). The reflection of these points across the x-axis would be (-2,-3) and (2,-3).
The two reflected points (-2,-3) and (2,-3) lie on the same horizontal line with a y-coordinate of -3. Therefore, the distance between the two points is 2 units.
Therefore, the correct answer is D. 4 units.
The original line contains the points (-2,3) and (2,3). The reflection of these points across the x-axis would be (-2,-3) and (2,-3).
The two reflected points (-2,-3) and (2,-3) lie on the same horizontal line with a y-coordinate of -3. Therefore, the distance between the two points is 2 units.
Therefore, the correct answer is D. 4 units.
A line segment has endpoints (2,-1) and (5,-4). What are the new endpoints after rotating the segment 90 degrees clockwise?
A. (-2, 1) and (-5, 4)
B. (2, -1) and (4,5)
C. (-1, -2) and (-4,-5)
D. (-2,-1) and (-5,-4)
A. (-2, 1) and (-5, 4)
B. (2, -1) and (4,5)
C. (-1, -2) and (-4,-5)
D. (-2,-1) and (-5,-4)
To rotate a point 90 degrees clockwise, we need to swap the x and y coordinates and change the sign of the new x coordinate.
For the first endpoint (2, -1):
- Swapping the x and y coordinates gives us (-1, 2).
- Changing the sign of the new x coordinate gives us (-1, -2).
For the second endpoint (5, -4):
- Swapping the x and y coordinates gives us (-4, 5).
- Changing the sign of the new x coordinate gives us (-4, -5).
Therefore, the new endpoints after rotating the line segment 90 degrees clockwise are (-1, -2) and (-4, -5).
The correct answer is C. (-1, -2) and (-4, -5).
For the first endpoint (2, -1):
- Swapping the x and y coordinates gives us (-1, 2).
- Changing the sign of the new x coordinate gives us (-1, -2).
For the second endpoint (5, -4):
- Swapping the x and y coordinates gives us (-4, 5).
- Changing the sign of the new x coordinate gives us (-4, -5).
Therefore, the new endpoints after rotating the line segment 90 degrees clockwise are (-1, -2) and (-4, -5).
The correct answer is C. (-1, -2) and (-4, -5).
A rectangle has a side that is 10 units long. How long will this side be after the figure is translated down 4 units and to the right 5 units?
__ units
__ units
If a rectangle has a side that is 10 units long, the length of that side will remain the same after a translation. Translating the figure down 4 units and to the right 5 units will only change its position, not its size.
Therefore, the length of the side will still be 10 units.
The side will be 10 units long.
Therefore, the length of the side will still be 10 units.
The side will be 10 units long.
A rectangle with a vertex at (8, -2) is translated 3 units down. What are the coordinates of this vertex after it is translated?
To translate the rectangle 3 units down, we need to subtract 3 from the y-coordinate of the vertex.
The original vertex is (8, -2). Subtracting 3 from the y-coordinate gives us -2 - 3 = -5.
Therefore, the coordinates of the vertex after it is translated 3 units down are (8, -5).
The original vertex is (8, -2). Subtracting 3 from the y-coordinate gives us -2 - 3 = -5.
Therefore, the coordinates of the vertex after it is translated 3 units down are (8, -5).
Coordinates: H (-3, 6), I (-1, 4), J (-1, 1), K (-4, 1), L (-5, 4)
Translated the figure HIJKL 3 units to the left. Which of the following would be a vertex in the translated figure?
A. (-6, 6)
B. (2,4)
C. (-1,-2)
D. (-7, 4)
Translated the figure HIJKL 3 units to the left. Which of the following would be a vertex in the translated figure?
A. (-6, 6)
B. (2,4)
C. (-1,-2)
D. (-7, 4)
To translate a figure 3 units to the left, we subtract 3 from the x-coordinates of each vertex.
The original vertices are:
H (-3, 6)
I (-1, 4)
J (-1, 1)
K (-4, 1)
L (-5, 4)
After translating 3 units to the left, the new vertices would be:
H (-3 - 3, 6) = (-6, 6)
I (-1 - 3, 4) = (-4, 4)
J (-1 - 3, 1) = (-4, 1)
K (-4 - 3, 1) = (-7, 1)
L (-5 - 3, 4) = (-8, 4)
Among the given options, the vertex that matches one of the translated coordinates is:
A. (-6, 6)
Therefore, the correct answer is A. (-6, 6).
The original vertices are:
H (-3, 6)
I (-1, 4)
J (-1, 1)
K (-4, 1)
L (-5, 4)
After translating 3 units to the left, the new vertices would be:
H (-3 - 3, 6) = (-6, 6)
I (-1 - 3, 4) = (-4, 4)
J (-1 - 3, 1) = (-4, 1)
K (-4 - 3, 1) = (-7, 1)
L (-5 - 3, 4) = (-8, 4)
Among the given options, the vertex that matches one of the translated coordinates is:
A. (-6, 6)
Therefore, the correct answer is A. (-6, 6).
1 answer