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Geometry B
Review 6-1, 6-2, 6-6
Solve each proportion for the variable.
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7. Joe is 72 inches tall. The scale factor of Joe to the image of Joe on a painting is
¼. What is Joe’s height in the painting?
8. The ratio of the measures of three sides of a triangle is 8:7:5. Its perimeter is 240
feet. Find the measures of the sides.
9. The ratio of the measures of the sides of a triangle is 6:8:10. Its perimeter is 72
inches. Find the measures of the sides.
10. The ratio of the measures of the three angles is 2:5:3. Find the measure of the
angles.
11. The ratio of the measures of the three angles is 3:5:7. Find the measure of the
angles.
12. A breakfast cereal contains wheat, rice, and oats in the ratio 6:2:4. If the
manufacturer makes a mixture weighing 180 pounds, how many pounds of wheat
will be used?
13. A breakfast cereal contains wheat, rice, and oats in the ratio 12:4:8. If the
manufacturer makes a mixture weighing 180 pounds, how many pounds of wheat
will be used?
14. A 6 inch by 8 inch photo is enlarged to produce a 9 inch by 12 inch photo. Find
the scale factor of the dilation.
15. If the 6 inch by 8 inch photo is reduced to produce a 3 inch by 4 inch photo, find
the scale factor of the dilation.
16. Find the height of the flag pole.
17. Find the height of the tree.
18. Joe is making a model of his car that is 84 inches long. The scale factor of the
car to the model is ¾. How long is the model?
19. If a person 5 tall casts a shadow 3.5 long, how tall is a tree which casts a
shadow 22 feet in length?
20. A tree casts a shadow 10 ft long. A boy standing next to the tree casts a shadow
2.5 ft. long. The triangle shown for the tree and its shadow is similar to the triangle
shown for the boy and his shadow. If the boy is 5.5 feet tall how tall is the tree?
The triangles below are similar. Find x and the scale factor of the larger triangle to
the smaller triangle and write a similarity statement for the two triangles.
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x
x+2
2x
The triangles below are similar. Solve for x and y. Determine the scale factor from
the smaller to the larger .
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27. The dilation D: (x, y)  (0.5x, 0.5y) has been applied to the polygon S(–8, 6),
T(–9, 5), U(7, 13). What are the coordinates of the image points?
28. The dilation D: (x, y)  (0.7x, 0.7y) has been applied to the polygon S(–3, 4),
T(–12, 6), U(9, 3). What are the coordinates of the image points?
Decide if the triangles are similar. If so write a similarity statement, if not write not
similar.
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Q
35. The coordinates of ∆PMN are P(3, 5), M(4, −8), and N(−9, 6). After a dilation,
the image of P is (27, 45). What are the coordinates of the image of M?
36. The coordinates of ∆PMN are P(5, 6), M(13, −4), and N(−9, 7). After a dilation,
the image of P is (55, 66). What are the coordinates of the image of M?
The figures are similar. What is the scale factor from the smaller figure to the
larger figure. Determine if it is an enlargement or reduction.
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Graph ∆ABC with coordinates of A(4, 12), B(–12, 8) and C(4, –16). The dilation
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of ∆ABC onto ∆ABC is . Graph ∆ABC, and describe the dilation as an
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enlargement or reduction.