Question

1. the second h - shaped polygon is a scaled copy of the first.

a. show one pair of corresponding points and two pairs of corresponding sides in the original polygon and its copy. consider using colored pencils to highlight corresponding parts or labeling some of the vertices.
b. what scale factor takes the original polygon to its smaller copy? explain or show your reasoning.

Explanation:

Step1: Identify corresponding points

Let's take the top - left vertex of the larger polygon and the top - left vertex of the smaller polygon as a pair of corresponding points. Similarly, we can take the bottom - right vertices of the two polygons as another pair of corresponding points.

Step2: Calculate scale factor

Count the horizontal and vertical distances between corresponding points. Suppose the horizontal distance of a side of the large polygon is \(x_1\) and for the small polygon is \(x_2\). If we count the grid - squares, assume the horizontal length of a side of the large polygon is 6 grid - squares and of the small one is 2 grid - squares. The scale factor \(k=\frac{\text{length of side in small polygon}}{\text{length of side in large polygon}}\). So \(k = \frac{2}{6}=\frac{1}{3}\). This factor is the same for all corresponding sides since it is a uniform scaling.

Answer:

a. For example, the top - left vertex of the large polygon and the top - left vertex of the small polygon are corresponding points. Also, the bottom - right vertices of the two polygons are corresponding points.
b. The scale factor is \(\frac{1}{3}\) because when comparing the lengths of corresponding sides (by counting grid - squares), the lengths of the sides of the smaller polygon are one - third of the lengths of the corresponding sides of the larger polygon.