(geometry only answer if u know) 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

option: b is correct.

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

Step-by-step explanation:

Yes, the rectangle EFGH is a result of dilation of rectangle ABCD with a center of dilation 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 ratuio of the sides of the image to the pre-image rectangle.

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:

Hence the scale factor is: 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 ).

Hence option: b is correct.

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

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