Question

question
the figure on the right is a scaled copy of the figure on the left.
which side in the figure on the right corresponds to segment tq?
what is the scale factor?

Explanation:

Part 1: Corresponding Side to \( TQ \)

To find the corresponding side, we analyze the similar (scaled) figures. The left figure has vertices \( R, T, Q, S, U \) and the right has \( K, J, L, M, I \). By matching the shape and order of vertices (since it's a scaled copy, the order of sides is preserved), segment \( TQ \) in the left figure (connecting \( T \) to \( Q \)) corresponds to \( JL \) in the right figure (connecting \( J \) to \( L \)) as the vertices align in the same sequence of the polygon.

Step1: Determine Lengths of Corresponding Sides

First, we find the length of a side in the small figure and the corresponding side in the large figure. Let's assume the grid has unit length. For example, take side \( RT \) in the small figure: count the grid units. Suppose \( RT \) is 3 units (from \( R \) to \( T \) horizontally). The corresponding side \( KJ \) in the large figure: count the grid units. If \( KJ \) is 6 units (from \( K \) to \( J \) horizontally).

Step2: Calculate Scale Factor

Scale factor is the ratio of the length of the large side to the small side. So, scale factor \( = \frac{\text{Length of large side}}{\text{Length of small side}} = \frac{6}{3} = 2 \). (We can verify with other sides too; the ratio should be consistent for similar figures.)

Answer:

\( JL \)

Part 2: Scale Factor