Question

Is rectangle EFGH the result of a dilation of rectangle ABCD with a center of dilation at the origin

Answer 1

Yes, because both figures are rectangles and all rectangles are similar. Option B is correct option.

According to the statement

We have given that the two rectangles EFGH and ABCD and we have show that the these rectangles Are dilation at origin or not.

So, According to the given diagram

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

Also The scale factor of the dilation is greater than one as the image is bigger than the pre-image i.e. there is a stretch.

The scale factor could be calculated by the ratio of the sides of the image to the pre-image rectangle.

According to the diagram In Rectangle ABCD:

Its vertices have coordinates A(-3,3), B(3,3), C(3,0) and D(-3,0).

Now consider rectangle EFGH:  

Its vertices have coordinates E(-4,4), F(4,4), G(4,0) and H(-4,0).

Hence the scale factor is becomes from these values is:

EF/AB = EH/AD = FG/BC = HG/DC = 4/3.

Hence the scale factor becomes 4/3.

Also

∠A=∠B=∠C=∠D=∠E=∠F=∠G=∠H=90°

( When a shape is dilated the two shapes are similar.And similar shapes have equal interior angles , corresponding sides are proportional ).

So, Yes, because both figures are rectangles and all rectangles are similar. Option B is correct option.

Learn more about center of dilation of rectangle here brainly.com/question/17986580

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