Lesson 4: Practice Problems

Problem 1

Select all the statements that must be true for any scaled copy of Polygon .

Angle measures of Polygon P clockwise from bottom left, in degrees, 90, 125, 35, 250, 80, 135.

  1. The side lengths are all whole numbers.

  2. The angle measures are all whole numbers.

  3. has exactly 1 right angle.

  4. If the scale factor between and is , then each side length of is multiplied by to get the corresponding side length of .

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

  6. has 2 acute angles and 3 obtuse angles.

Problem 2

Here is Quadrilateral .

Quadrilateral ABCD is on a grid. Point a is 2 units right and 4 units down from the edge of the grid. Point B is 2 units right and 2 units up from point A. Point C is 6 units right from point A. Point D is 2 units right and 4 units down from point A.

Quadrilateral is a scaled copy of Quadrilateral . Point corresponds to , to , to , and to .

If the distance from to is 3 units, what is the distance from to ? Explain your reasoning.

Problem 3

Figure 2 is a scaled copy of Figure 1.

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

    Two 4-sided figures in a coordinate plane labeled Figure 1 and Figure 2. Figure 1 has four points. Point A is 3 units to the left and 2 units up from the bottom-right point. The top-right point is 1 unit up and 3 units to the right of point A. Point C is 1 unit down and 1 unit to the left of the top-right point. The bottom-right point is 1 unit to the right and 2 units down from point C. The bottom-right point is directly below the top-right point. Lines are drawn connecting point A to the top-right point, the top-right to C, C to the bottom-right point, and the bottom-right to A. Figure 2 also has four points. The left-most point is 9 units to the left and 6 units up from point S. Point Q is 3 units up and 9 units to the right of the left-most point. A fourth point is 3 units down and 3 units to the left of point Q. Point S is 3 units to the right and 6 units down from the fourth point. Point S is directly below point Q. Lines are drawn connecting the left-most point to Q, Q to the fourth point, the fourth point to S, and S to the left-most point.

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

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

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

Problem 4 From Unit 2 Lesson 4

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.