Scaled Relationships

Multiple Choice

Select **all** the statements that must be true for _any_ scaled copy Q of Polygon P.

• Q has exactly 1 right angle.

• If the scale factor is 2, each angle in P is multiplied by 2 to get the corresponding angle in Q.

• If the scale factor between P and Q is $$\frac15$$ , then each side length of P is multiplied by $$\frac15$$ to get the corresponding side length of Q.

• The side lengths are all whole numbers.

• The angle measures are all whole numbers.

Open Ended

Quadrilateral ABCD is on a grid. Quadrilateral $$PQRS$$ is a scaled copy of quadrilateral $$ABCD$$ . Point $$P$$ corresponds to $$A$$ , $$Q$$ to $$B$$ , $$R$$ to $$C$$ , and $$S$$ to $$D$$ . If the distance from $$P$$ to $$R$$ is 3 units, what is the distance from $$Q$$ to $$S$$ ? Explain your reasoning.

Multiple Choice

What is the distance between the points P and R in Figure 2, which correspond to points A and C in Figure 1?

• 1.41
• 1.00
• 0.50
• 2.00

Multiple Choice

Identify the points in Figure 1 that correspond to the points Q and S in Figure 2. Label them B and D. What is the distance between B and D?

• The distance between B and D is 4 units.
• The distance between B and D is 8 units.
• The distance between B and D is 6 units.
• The distance between B and D is 2 units.

Multiple Choice

What is the scale factor that takes Figure 1 to Figure 2?

• 4
• 2
• 5
• 3

Multiple Choice

(G) and (H) are two points on Figure 1, but they are not shown. The distance between (G) and (H) is 1. What is the distance between the corresponding points on Figure 2?

• 3
• 0.5
• 1
• 2

Multiple Choice

To make 1 batch of lavender paint, the ratio of cups of pink paint to cups of blue paint is 6 to 5. Find two more ratios of cups of pink paint to cups of blue paint that are equivalent to this ratio.

• 8:7
• 10:8
• 14:12
• 12:10, 18:15

Multiple Choice

Which of the following observations would help you decide that two polygons are not scaled copies?

• The corresponding angles are not equal or the ratios of corresponding side lengths are not constant.
• The polygons have the same perimeter.
• The polygons have the same color.
• The polygons are both triangles.

Multiple Choice

Kiran and Mai are standing at one corner of a rectangular field of grass looking at the diagonally opposite corner. Kiran says that if the field were twice as long and twice as wide, then it would be twice the distance to the far corner. Mai says that it would be more than twice as far, since the diagonal is even longer than the side lengths. Do you agree with either of them?

• I agree with Kiran.
• The distance would be exactly twice.
• Kiran is wrong; the distance is halved.

Draw

On the grid, draw a scaled copy of quadrilateral ABCD with a scale factor $$\frac{2}{3}$$ .