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′(3, 3), B′(9, 3), C′(9, 6), and D′(3, 6). Determine the scale factor used to create the image.

3
2
one half
one third

Answer 1

To determine the scale factor used to dilate polygon ABCD to A′B′C′D′, we can compare the corresponding side lengths.

The distance between A(1, 1) and B(3, 1) is 2 units, and the distance between A′(3, 3) and B′(9, 3) is 6 units, so the horizontal side has been scaled by a factor of 6/2 = 3.

Similarly, the distance between A(1, 1) and D(1, 2) is 1 unit, and the distance between A′(3, 3) and D′(3, 6) is 3 units, so the vertical side has been scaled by a factor of 3/1 = 3.

Since both scaling factors are equal to 3, the overall scale factor used to dilate the polygon is 3. Answer: 3.

Answer 2

The answer to your problem would be 3