Question

Is rectangle EFGH the result of a dilation of rectangle ABCD with a center of dilation at the origin? Why or why not?

a.Yes, because corresponding sides are parallel and have lengths in the ratio 1/4

b.Yes, because both figures are rectangles and all rectangles are similar.

c.No, because the center of dilation is not at (0, 0).

d.No, because corresponding sides have different slopes

Answer 1

Option B.

Explanation:

In the figure attached two rectangles ABCD and EFGH have been given.

Rectangle ABCD has been dilated by the origin to form rectangle EFGH.

Ratio of the sides CD and GH =
`(3-(-3))/(4-(-4))`

=
`(6)/(8)`

=
`(3)/(4)`

Similarly ratio of the sides AD and EH =
`(3)/(4)`

Therefore, the corresponding sides of the rectangles given have the same ratio of
`(3)/(4)`.

Since both the figures are rectangles and all rectangles are similar, so Option B. will be the answer.

Answer 2

Option B is right answer.

Explanation:

Yes, it is true hat the rectangle EFGH is a result of dilation of rectangle ABCD with a center of dilation at the origin.

Also according to the given image, we can see that the scale factor of the dilation is greater than one as the new image is bigger than the pre-image.

Also, we can see is that ∠A=∠B=∠C=∠D=∠E=∠F=∠G=∠H=90°

So, we can say that option B is true - Yes, because both figures are rectangles and all rectangles are similar.