Question

On a coordinate plane, Rectangles A B C D and E F G H are shown. The length of side A B is 6 units and the length of side B C is 3 units. The length of side E F is 8 units and the length of side F G is 4 units. Is rectangle EFGH the result of a dilation of rectangle ABCD with a center of dilation at the origin? Why or why not? Yes, because corresponding sides are parallel and have lengths in the ratio Four-thirds Yes, because both figures are rectangles and all rectangles are similar. No, because the center of dilation is not at (0, 0). No, because corresponding sides have different slopes

Answer 1

A. Yes, because corresponding sides are parallel and have lengths in the ratio Four-thirds

Explanation:

Answer 2

Yes, because corresponding sides are parallel and have lengths in the ratio Four-thirds.

Explanation:

Dilation is a transformation process in which the dimensions of a given figure are resized to produce an image with the same shape. This is done with respect to a scale factor and center of dilation.

In the given question, the center of dilation is at the middle of side DC of rectangle ABCD (i.e on side DC).

Given that the scale factor is
`(4)/(3)`,

EF = HG =
`(4)/(3)` × AB =
`(4)/(3)` × 6 = 8 units

FG = EH =
`(4)/(3)` × BC =
`(4)/(3)` × 3 = 4 units

Therefore, rectangle EFGH is the result of dilation of ABCD.