Question

the figure on the right is a scaled copy of the figure on the left. answer attempt 1 out of 99 which side in the figure on the right corresponds to segment ut? what is the scale factor?

Explanation:

Step1: Identify corresponding sides

In scaled - copies, corresponding sides are in proportion. By observing the orientation and shape of the polygons, segment \(UT\) in the left figure corresponds to segment \(NK\) in the right figure.

Step2: Calculate the scale factor

Let's assume the length of \(UT\) (counting the grid units). If \(UT\) has a length \(l_1\) (say \(UT = 2\) units) and \(NK\) has a length \(l_2\) (say \(NK=4\) units). The scale factor \(k=\frac{l_2}{l_1}\).
Counting the units:

• For the left - hand polygon (smaller one), assume \(UT\) spans \(2\) grid units (horizontal or vertical, using the grid to measure).
• For the right - hand polygon (larger one), \(NK\) spans \(4\) grid units.

The scale factor \(k=\frac{\text{Length of corresponding side in scaled - copy}}{\text{Length of side in original}}=\frac{4}{2}=2\)

Answer:

• The side that corresponds to segment \(UT\) is \(NK\).
• The scale factor is \(2\).