Use the image to answer the question.
A coordinate plane with four quadrants showsthe x-axis ranging from negative 4 to 12 in increments of 1 and the y-axis from 1 to negative 16 in increments of 1. Points upper A, upper B, upper A prime, and upper B prime are plotted on quadrant 4. The plotted points are as follows: Upper A is left parenthesis 1 comma negative 3 right parenthesis and upper B is left parenthesis 2 comma negative 4 right parenthesis. The points are joined by a line. Upper A prime is plotted as left parenthesis 4 comma negative 12 right parenthesis and upper B prime as left parenthesis 8 comma negative 16 right parenthesis. The points are joined by a line.
Determine the scale factor used in the dilation of line segment AB, centered at the origin.
(1 point)
Responses
14
Start Fraction 1 over 4 End Fraction
4
4
−4
negative 4
2
2
11 answers
Start Fraction 1 over 4 End Fraction
Question
Use the image to answer the question.
A coordinate plane with four quadrants shows an x axis capped with arrows ranging from negative 3 to 12 in 1 unit increments and a y axis capped with arrows ranging from 15 to negative 4 in 1 unit increments. Points upper A, upper B, upper A prime, and upper B prime are plotted in quadrant 1. Point upper A is plotted as left parenthesis 9 comma 9 right parenthesis and point upper B is plotted as left parenthesis 6 comma 6 right parenthesis. The points are plotted on a line segment. Point upper A prime is plotted as left parenthesis 3 comma 3 right parenthesis and upper B prime is plotted as left parenthesis 2 comma 2 right parenthesis. The points are plotted on a line segment.
Determine the scale factor used in the dilation of line segment AB, with a center point of dilation at the origin.
(1 point)
Responses
−3
negative 3
−13
negative Start Fraction 1 over 3 End Fraction
13
Use the image to answer the question.
A coordinate plane with four quadrants shows an x axis capped with arrows ranging from negative 3 to 12 in 1 unit increments and a y axis capped with arrows ranging from 15 to negative 4 in 1 unit increments. Points upper A, upper B, upper A prime, and upper B prime are plotted in quadrant 1. Point upper A is plotted as left parenthesis 9 comma 9 right parenthesis and point upper B is plotted as left parenthesis 6 comma 6 right parenthesis. The points are plotted on a line segment. Point upper A prime is plotted as left parenthesis 3 comma 3 right parenthesis and upper B prime is plotted as left parenthesis 2 comma 2 right parenthesis. The points are plotted on a line segment.
Determine the scale factor used in the dilation of line segment AB, with a center point of dilation at the origin.
(1 point)
Responses
−3
negative 3
−13
negative Start Fraction 1 over 3 End Fraction
13
Start Fraction 1 over 3 End Fraction
Triangle ABC has vertices point A(−2,−2), point B(−4,−3), and point C(−2,−5). Find the coordinates of A′, B′, and C′ after a dilation with a scale factor of 3
and a center point of dilation at the origin.(2 points)
A′= (
)
B′= (
)
C′= (
)
and a center point of dilation at the origin.(2 points)
A′= (
)
B′= (
)
C′= (
)
To find the coordinates of A', B', and C' after a dilation with a scale factor of 3 and a center point of dilation at the origin, you simply need to multiply the coordinates of the original points by the scale factor.
For point A(-2, -2):
A' = (-2*3, -2*3) = (-6, -6)
For point B(-4, -3):
B' = (-4*3, -3*3) = (-12, -9)
For point C(-2, -5):
C' = (-2*3, -5*3) = (-6, -15)
Therefore, the coordinates of A', B', and C' after the dilation are:
A' = (-6, -6)
B' = (-12, -9)
C' = (-6, -15)
For point A(-2, -2):
A' = (-2*3, -2*3) = (-6, -6)
For point B(-4, -3):
B' = (-4*3, -3*3) = (-12, -9)
For point C(-2, -5):
C' = (-2*3, -5*3) = (-6, -15)
Therefore, the coordinates of A', B', and C' after the dilation are:
A' = (-6, -6)
B' = (-12, -9)
C' = (-6, -15)
Transformations and Similarity Unit Test
4 of 154 of 15 Items
Question
Use the image to answer the question.
An illustration shows an 11 by 9 grid with 4 triangles on it. Figure 1 is an obtuse triangle that extends from top of the 2nd to end of 5th rows, starting in the 4th and ending in the 5th columns. The perpendicular line is 3 units down the left side of column 4, from the 2nd to 4th rows. From that point the next side runs to the corner of row 5, column 5. Figure 2 is an isosceles triangle that extends from the top of 3rd to the bottom of the 4th row, and across columns 7 and 8. The base extends for 2 units and the perpendicular height is 2 units. Figure 3 is an inverted obtuse triangle that extends from approximately the 5th to approximately the end of the 7th rows, and approximately the 1st to 6th columns. The triangle is inclined at an angle and the vertex is between the 3rd and 4th columns at the bottom of the 7th row. Figure 4 extends from the top of 6th to the bottom of 8th rows, in the 8th and 9th columns. The perpendicular line is 3 units high along the left side of the 8th column. A vertex is at the bottom of row 7, column 9.
Which figure is similar to Figure 1?(1 point)
Figure
4 of 154 of 15 Items
Question
Use the image to answer the question.
An illustration shows an 11 by 9 grid with 4 triangles on it. Figure 1 is an obtuse triangle that extends from top of the 2nd to end of 5th rows, starting in the 4th and ending in the 5th columns. The perpendicular line is 3 units down the left side of column 4, from the 2nd to 4th rows. From that point the next side runs to the corner of row 5, column 5. Figure 2 is an isosceles triangle that extends from the top of 3rd to the bottom of the 4th row, and across columns 7 and 8. The base extends for 2 units and the perpendicular height is 2 units. Figure 3 is an inverted obtuse triangle that extends from approximately the 5th to approximately the end of the 7th rows, and approximately the 1st to 6th columns. The triangle is inclined at an angle and the vertex is between the 3rd and 4th columns at the bottom of the 7th row. Figure 4 extends from the top of 6th to the bottom of 8th rows, in the 8th and 9th columns. The perpendicular line is 3 units high along the left side of the 8th column. A vertex is at the bottom of row 7, column 9.
Which figure is similar to Figure 1?(1 point)
Figure
Figure 4 is similar to Figure 1.
Use the image to answer the question.
An illustration shows a 15 by 12 grid with 4 triangles and a parallelogram on it. Figure 1 is an isosceles triangle in the 3rd to the 4th rows, 6th and 7th columns. The base is 2 units and the perpendicular height is 2 units. Figure 2 is an inverse isosceles triangle, and extends from the top of the 3rd to the bottom of the 5th row, within the 10th and 11th columns. The base extends for 2 units and the perpendicular height is 3 units. Figure 3, a parallelogram, has the top side as 2 units on the top of row 6, columns 6 and 7. The bottom side is 2 units across the base of the 8th row, columns 3 and 4. Figure 4 is a triangle, extending from the top of the 8th row to the bottom of the 10th row, columns 7 to 9. The base is 3 units in length, and the perpendicular height is 3 units. Figure 5 is an isosceles triangle with the base as 2 units on the right side of 13th column, and the perpendicular height as 2 units.
Which figure is similar to Figure 1?(1 point)
Figure
An illustration shows a 15 by 12 grid with 4 triangles and a parallelogram on it. Figure 1 is an isosceles triangle in the 3rd to the 4th rows, 6th and 7th columns. The base is 2 units and the perpendicular height is 2 units. Figure 2 is an inverse isosceles triangle, and extends from the top of the 3rd to the bottom of the 5th row, within the 10th and 11th columns. The base extends for 2 units and the perpendicular height is 3 units. Figure 3, a parallelogram, has the top side as 2 units on the top of row 6, columns 6 and 7. The bottom side is 2 units across the base of the 8th row, columns 3 and 4. Figure 4 is a triangle, extending from the top of the 8th row to the bottom of the 10th row, columns 7 to 9. The base is 3 units in length, and the perpendicular height is 3 units. Figure 5 is an isosceles triangle with the base as 2 units on the right side of 13th column, and the perpendicular height as 2 units.
Which figure is similar to Figure 1?(1 point)
Figure
Figure 5 is similar to Figure 1.
Use the image to answer the question.
An illustration shows 2 trapezoids labeled Figure 1 and Figure 2 placed on a 12 column by 6 row grid. Figure 2 is smaller and a mirror image of Figure 1. Figure 1 shows the top left vertex on the top of the 3rd row and the start of the 3rd column, the top right vertex is on the top of the 3rd row and the start of the 5th column, the bottom left vertex is on the bottom of the 4th row and the start of 3rd column, and the bottom right vertex is on the bottom of the 4th row and the end of the 5th column. Figure 2 shows the top left vertex on the middle of the 3rd row and the middle of the 9th column, the top right vertex on the middle of the 3rd row and the end of the 10th column, the bottom left vertex on the end of the 4th row and on the 8th column, and the bottom right vertex on the end of the 4th row and end of the 10th column.
Describe the sequence of transformations that exhibits the similarity between Figures 1 and 2.
(1 point)
Responses
rotation and dilation
rotation and dilation
translation and dilation
translation and dilation
reflection and translation
reflection and translation
dilation and reflection
An illustration shows 2 trapezoids labeled Figure 1 and Figure 2 placed on a 12 column by 6 row grid. Figure 2 is smaller and a mirror image of Figure 1. Figure 1 shows the top left vertex on the top of the 3rd row and the start of the 3rd column, the top right vertex is on the top of the 3rd row and the start of the 5th column, the bottom left vertex is on the bottom of the 4th row and the start of 3rd column, and the bottom right vertex is on the bottom of the 4th row and the end of the 5th column. Figure 2 shows the top left vertex on the middle of the 3rd row and the middle of the 9th column, the top right vertex on the middle of the 3rd row and the end of the 10th column, the bottom left vertex on the end of the 4th row and on the 8th column, and the bottom right vertex on the end of the 4th row and end of the 10th column.
Describe the sequence of transformations that exhibits the similarity between Figures 1 and 2.
(1 point)
Responses
rotation and dilation
rotation and dilation
translation and dilation
translation and dilation
reflection and translation
reflection and translation
dilation and reflection
The sequence of transformations that exhibits the similarity between Figures 1 and 2 is: rotation and dilation.