Question

Polygon ABCD with vertices at A(1, −1), B(3, −1), C(3, −2), and D(1, −2) is dilated to create polygon A′B′C′D′ with vertices at A′(2, −2), B′(6, −2), C′(6, −4), and D′(2, −4). Determine the scale factor used to create the image. 3 2 one half one third

Answer 1

Explanation:

To determine the scale factor used to create the image, we can compare the corresponding side lengths of the original polygon ABCD and the image polygon A′B′C′D′.

Let's start with the distance between points A and B in polygon ABCD.

Distance between A and B in ABCD = 3 - 1 = 2

Distance between corresponding points A' and B' in A'B'C'D' = 6 - 2 = 4

So, the side length AB in the image is twice the length of the corresponding side in the original polygon.

We can check the other side lengths as well:

Distance between B and C in ABCD = 1

Distance between corresponding points B' and C' in A'B'C'D' = 2

So, the side length BC in the image is twice the length of the corresponding side in the original polygon.

Distance between C and D in ABCD = 2

Distance between corresponding points C' and D' in A'B'C'D' = 2

So, the side length CD in the image is the same as the length of the corresponding side in the original polygon.

Distance between D and A in ABCD = 2

Distance between corresponding points D' and A' in A'B'C'D' = 2

So, the side length DA in the image is the same as the length of the corresponding side in the original polygon.

Since the side lengths AB and BC in the image are twice the lengths of the corresponding sides in the original polygon, we can conclude that the scale factor used to dilate the polygon is 2.

Therefore, the answer is: 2.