Unit 6 Dilations Homework
Name __________________________________
Practice 6A
1. ΔPZG has vertices P(2,0), Z(-1,0.5), and G(1,-2). What are the coordinates of the image of P for a dilation with center
(0,0) and scale factor 3?
2. A(-3,2) is a preimage point in a dilation with scale factor 3:2 and center at the origin. What are the coordinates of the
corresponding image point?
3. In a dilation with center at the origin, a point on the preimage is at (-3,6) and the corresponding point on the image is at
(-4,8). What is the scale factor?
4. ΔPZG has vertices P(2,0), Z(-1,0.5), and G(1,-2). What are the coordinates of the image of G for a dilation with center
(0,0) and scale factor 3:4?
5. ΔRST is mapped onto ΔR’S’T’ with center C. CR’:CR = 3:5. Which best describes the dilation?
A. ΔR’S’T’ is an enlargement of ΔRST. The scale factor is 5:3.
B. ΔR’S’T’ is a reduction of ΔRST. The scale factor is 5:3.
C. ΔR’S’T’ is congruent to ΔRST.
D. ΔR’S’T’ is an enlargement of ΔRST. The scale factor is 3:5.
E. ΔR’S’T’ is a reduction of ΔRST. The scale factor is 3:5.
Practice 6B
1. What is the value of x?
3. What is the value of x?
2. MB=2, OQ=4, NP=10, and MP=20. What is MO?
4. What is the value of y?
5. How long is segment EF?
5. The legs of a right triangle have lengths 7 and 24. The bisector of the right angle divides the hypotenuse into two
segments. What is the length of the shorter segment of the hypotenuse to the nearest tenth?
Unit 6 Dilations Homework
Name __________________________________
Practice 6C
1. Two regular hexagons have sides in the ratio 3:5. The area of the smaller hexagon is 81 m 2. In square meters, what is
the area of the larger hexagon?
2. Two similar polygons have areas in the ratio 9:16. The perimeter of the larger polygon is 900. What is the perimeter of
the smaller polygon?
3. Two triangles are similar. Their perimeters have the ratio 1:3. In square feet, what is the area of the smaller triangle if
the area of the larger triangle is 486 ft2?
4. What is the ratio of the areas of similar triangles whose similarity ratio is 4:9?
5. The volumes of two similar pyramids are 1331 cm3 and 2744 cm3. What is the ratio of their heights?
Practice 6D
1. A rectangle has a perimeter of 104 in. A similar rectangle has a perimeter of 286 in. The area of the smaller rectangle is
672 in.2. In square inches, what is the area of the larger rectangle?
2. The area of a polygon is 3267 cm2. The area of a similar polygon is 9075 cm2. The perimeter of the larger polygon is 270
cm. In centimeters, what is the perimeter of the smaller one?
3. The area of a regular decagon is 50 cm2. What is the area of a regular decagon with sides four times the sides of the
smaller decagon?
4. A regular octagon has a side length of 8 m and an area of approximately 309 m2. The side length of another regular
octagon is 4 m. What is the approximate area of the smaller octagon?
5. A lawn chair weighs 8 lb. A child’s lawn chair has dimensions exactly one half those of the larger chair. How many
pounds does the child’s chair weigh?
Unit 6 Dilations Homework
Name __________________________________
Practice 6E
1. Let the numbers represent the lengths of the sides of a triangle. Which of the triangles are right triangles?
A. 5, 8, 13
B. 2.7, 3.6, 4.5
C. 1, 2, 3
D. 7.5, 8.5, 10.5
E. 18, 24, 31
2. A farmer’s land has the shape and dimensions shown in the coordinate grid. Each unit on
the grid represents 1 km. What is the perimeter of the farmer’s land to the nearest tenth
of a kilometer?
3. A small rectangular park measures 200 m by 300 m. To the nearest meter, how much shorter is it if you walk along a
diagonal to get to the opposite corner than if you walk along two adjacent sides?
4. Which of the following sets of side lengths is NOT a primitive Pythagorean triple?
A. 3, 4, 5
B. 5, 12, 13
C. 16, 30, 34
D. 7, 24, 25
5. What is the value of x?
Practice 6F
1. What kind of triangle can be formed by side lengths 8, 10, and 12?
2. What kind of triangle can be formed by side lengths 10, 24, and 26?
3. What kind of triangle can be formed by side lengths 4, 8, and 10?
4. What kind of triangle can be formed by side lengths 2, 5, and 7?
5. Two sides of a triangle are 4 and 6. Which length for the third side will make the triangle obtuse?
A. 4
B. 6
C. 8
D. 10
Unit 6 Dilations Homework
Name __________________________________
Practice 6G
1. A dilation maps ΔABC onto ΔA’B’C’ with a scale factor of 0.3. If A’B’ = 312 m and B’C’ = 200 m, what is AB in meters?
2. A dilation maps ΔCDE onto ΔC’D’E’. If CD = 7.5 ft, CE = 15 ft, D’E’ = 3.25 ft, and C’D’ = 2.5 ft, what is DE in feet?
3. A dilation maps ΔXYZ onto ΔX’Y’Z’. If XY = 4 m, YZ = 29 m, X’Z’ = 28.7 m, and Y’Z’ = 29.145 m, what is X’Y’ in meters?
4. ΔPQR is mapped onto ΔP’Q’R’ by a dilation with center C and a scale factor 4:5. If QR = 18 m, PQ = 15 m, and PR = 20 m,
what is the length of segment Q’R’?
5. ΔPQR is mapped onto ΔP’Q’R’ by a dilation with center C and a scale factor 4:5. If QR = 18 m, PQ = 15 m, and PR = 20 m,
what is the length of segment P’R’?
Practice 6H
1. The surface areas of two similar cylinders are 6π ft2 and 54π ft2. The volume of the smaller cylinder is 2π ft3. What is the
volume in cubic feet of the larger cylinder?
2. A model of a historical home has dimensions that are one fifteenth the dimensions of the actual home. The area of a
window in the model is 2 cm2. What is the area in square centimeters of the corresponding window in the actual home?
3. The volumes of two similar rectangular prisms are 64 cm3 and 1000 cm3. The surface area of the smaller figure is 112
cm2. What is the surface area in square centimeters of the larger figure?
4. Sphere B has 4 times the surface area of sphere A. How may times the volume of sphere A is the volume of sphere B?
5. What is the ratio of the surface areas of similar solids whose similarity ratio is 3:5?
6. You are making a scale model of a building. The front of the actual building is 60 ft wide and 100 ft tall. The front of your
model is 3 ft by 5 ft. What is the scale factor?
7. You are 5 ft 6 in. tall. When your shadow is 6 ft long, the shadow of a sculpture is 30 ft long. How many feet tall is the
sculpture?
8. What is the value of x?
9. What is the value of x?
10. What is the perimeter of ΔABC?