Unit 1, Lesson 4
Scaled Relationships
Grade 7
Practice
Problem 1
Select all the statements that must be true for any scaled copy Q of Polygon P.
The side lengths are all whole numbers.
The angle measures are all whole numbers.
Q has exactly 1 right angle.
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.
If the scale factor is 2, each angle in P is multiplied by 2 to get the corresponding angle in Q.
Q has 2 acute angles and 3 obtuse angles.
Problem 2
Here is quadrilateral \(ABCD\).
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 \(PQRS\) 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.
to access Practice Problem Solutions.
Problem 3
Figure 2 is a scaled copy of Figure 1.
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.
- Identify the points in Figure 2 that correspond to the points \(A\) and \(C\) in Figure 1. Label them \(P\) and \(R\). What is the distance between \(P\) and \(R\)?
- 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 \(D\)?
- What is the scale factor that takes Figure 1 to Figure 2?
- \(G\) 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?