These questions are for the Transformations And Similarity Test. Please 100% and show work for questions 2, 5, 6, 13.
2. Triangle ABC has vertices point A (-3,-3), point B (5,-3), and point C (2, 4). Find the coordinates of A', B', and C' after a dilation with a scale factor of 2 and a center point dilation at the origin.
A' = _______
B' = _______
C' = _______
5. Use the image to answer the question. First triangle is 2 in. and 6.4 in. second triangle is x and 9.6 in. What is the length of x?
6. △RST ~ △XYZ. m∠R = 18°, m∠S = 75°. What are the measures of angles X,Y, and Z?
m∠X = ______
m∠Y = ______
m∠Z = ______
7. Consider the similar trianges below.
Part A:
The first triangle is, S, 5, 7, R, 8, T and the second triangle is, B, 14, C, A.
Find the scale factor.
The scale factor is: ____
Part B
Find the length of AC.
The length of AC is ____
8. Which of the following scale factors would result in a dilation that is a reduction?
A. 7/4
B. 1.5
C. 1/4
D. 5.25
9. Use the image to answer the question. Figure one is a couch, figure two is a laptop and figure three is power poles and figure four is an ant.
Which scale drawing is a dilation that increased the size of the original object it represents?
Figure ___
10. The black shape is a dilation of the purple shape. What is the scale factor of the dilation?
The scale factor is: ___
11. Which transformation involved the size of a figure being increased or decreased?
12. Choose all of the transformations that will result in the object changing size.
A. Dilation with a scale factor of 5.
B. Reflection over the y-axis
C. 90° counterclockwise rotation
D. Dilation with a scale factor of 0.75
E. Translation down 3 units and to the left 2 units.
13. If you want to dilate a figure that has a side length of 20 yards, to create a dilated image with a corresponding side length of 15 yards, what scale factor should you use?
A. 3/4 yard
B. 3/4
C. 5 yards
D. 4/3
14. Determine if each pair of the geometric figures is similar.
First pair is 42° and 82°
Second pair is L = 83°, M = 48°, N and second figure is C = 83° and D = 48° and E.
Third pair is 8 and 14 and the second figure is 5.6 and 3.2
15. Consider the graph shown below.
Part A
XYWZ. Write the coordinates of the point Y after a dilation with a scale factor of 4, centered at the origin. (_,_)
Part B
What are the coordinates of the point W after a dilation with a scale factor of 4, centered at the origin?
A. (-8,8)
B. (8,-8)
C. (-8, -8)
D. (8, 8)
2. To find the coordinates after a dilation with a scale factor of 2 and a center point dilation at the origin, you multiply the x and y coordinates of each point by the scale factor.
A' = (-3*2, -3*2) = (-6, -6)
B' = (5*2, -3*2) = (10, -6)
C' = (2*2, 4*2) = (4, 8)
A' = (-6, -6)
B' = (10, -6)
C' = (4, 8)
5. Using the properties of similar triangles, we can set up a proportion:
(2/6.4) = (x/9.6)
Cross-multiplying: 6.4x = 19.2
Dividing both sides by 6.4: x = 3 inches
The length of x is 3 inches.
6. Since △RST ~ △XYZ, corresponding angles are congruent.
m∠X = m∠R = 18°
m∠Y = m∠S = 75°
m∠Z = m∠T = 180° - m∠X - m∠Y = 180° - 18° - 75° = 87°
m∠X = 18°
m∠Y = 75°
m∠Z = 87°
7. Part A:
To find the scale factor, we can divide the corresponding side lengths:
SR / BC = 5 / 14 = 7 / 8
The scale factor is 7/8.
Part B:
AC = BC * (scale factor) = 14 * (7/8) = 98/8 = 12.25
The length of AC is 12.25.
8. C. 1/4
9. Figure four is a dilation that increased the size of the original object it represents.
Figure 4.
10. The scale factor is the ratio of corresponding side lengths. Since the black shape is a dilation of the purple shape, we can compare a side length of each shape to find the scale factor.
Scale factor = length of black shape / length of purple shape
Unfortunately, the specific figures were not provided, so the scale factor cannot be determined without additional information.
11. Dilation involves the size of a figure being increased or decreased.
12. A. Dilation with a scale factor of 5.
D. Dilation with a scale factor of 0.75.
13. To find the scale factor, we can set up a proportion:
(20/15) = (1/x)
Cross-multiplying: 20x = 15
Dividing both sides by 20: x = 15/20 = 3/4
The scale factor should be 3/4.
A. 3/4
14. For shapes to be similar, the corresponding angles must be congruent and the corresponding side lengths must be proportional.
First pair: The angles are not congruent (42° and 82°), so the figures are not similar.
Second pair: The angles are congruent (83° and 48°), so the figures are similar.
Third pair: The side lengths are not proportional (8/14 ≠ 5.6/3.2), so the figures are not similar.
The second pair is similar.
15. Part A:
To find the coordinates of Y after a dilation with a scale factor of 4, centered at the origin, you multiply the x and y coordinates of Y by the scale factor.
Y' = (2*4, 3*4) = (8, 12)
The coordinates of point Y after the dilation are (8, 12).
Part B:
To find the coordinates of W after a dilation with a scale factor of 4, centered at the origin, you multiply the x and y coordinates of W by the scale factor.
W' = (-2*4, -1*4) = (-8, -4)
The coordinates of point W after the dilation are (-8, -4).
C. (-8, -8)