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 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 of A', B', and C' after a dilation at the origin, we need to multiply the coordinates of each point by the scale factor.
Scale factor: k
A' = (-3*k, -3*k)
B' = (5*k, -3*k)
C' = (2*k, 4*k)
5. The length of the first triangle is 2 inches and the length of the second triangle is 9.6 inches. Let x represent the length of the second triangle.
Using the proportion: (2/6.4) = (x/9.6)
Cross-multiplying: 6.4x = 19.2
Dividing by 6.4: x = 3 inches
Therefore, the length of the second triangle (x) is 3 inches.
6. Since triangles △RST and △XYZ are similar, their corresponding angles are congruent.
m∠X = 18° (since m∠R = 18°)
m∠Y = 75° (since m∠S = 75°)
m∠Z = m∠T (since corresponding angles of similar triangles are congruent)
Therefore, m∠X = 18°, m∠Y = 75°, and m∠Z = m∠T.
7. Part A:
The scale factor can be found by comparing the corresponding side lengths of the triangles.
Scale factor = Length of corresponding side in triangle BCA / Length of corresponding side in triangle SRT
Scale factor = BC / SR
BC / SR = 14 / 7 = 2
The scale factor is 2.
Part B:
Since the scale factor is 2, the length of AC in triangle BCA is twice the length of ST in triangle SRT.
Length of AC = 2 * Length of ST = 2 * 8 = 16.
The length of AC is 16.
8. C. 1/4
9. Figure three is a dilation that increased the size of the original object it represents.
10. The scale factor is the ratio of corresponding side lengths of the two shapes. Without the figures provided, the scale factor cannot be determined.
11. Dilation
12. A. Dilation with a scale factor of 5.
D. Dilation with a scale factor of 0.75
13. To find the scale factor, divide the corresponding side lengths of the original figure and the dilated image.
Scale factor = Corresponding side length of dilated image / Corresponding side length of original figure
Scale factor = 15 / 20 = 0.75
The scale factor should be 0.75.
14. First pair: Not similar. The angles do not have the same measures.
Second pair: Similar. The angles have the same measures.
Third pair: Not enough information provided to determine if they are similar.
15. Part A:
To find the coordinates of point Y after a dilation with a scale factor of 4, centered at the origin, we need to multiply the coordinates of point Y by the scale factor.
Scale factor: k = 4
Coordinates of Y after dilation: (x*k, y*k) = (4*-2, 4*4) = (-8, 16)
Therefore, the coordinates of point Y after the dilation are (-8, 16).
Part B: The coordinates of point W after a dilation with a scale factor of 4, centered at the origin, would be (-8, -8). Therefore, the answer is C. (-8, -8).