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 both figures are rectangles and all rectangles are similar (B)

Question:

The complete question related to this found at (question Id: 2996738) is stated below:

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

Step-by-step explanation:

Coordinates of rectangle EFGH

E (-4,4), F(4,4), G(-4,0), H (4,0)

EF = 8

FG =4

GH= 8

HE= 4

Coordinates of rectangle ABCD

A (-3,3), B(3,3), C(-3,0), D (3,0)

AB = 6

BC = 3

CD = 6

DA = 3

Find attached the diagram.

Image = EFGH, pre-image = ABCD

Scale factor = (sides of the image)/(sides of the pre-image)

= 8/6 = 4/3

Similar shapes have same shapes but different sizes. From the result obtained, the two shapes are similar with different sizes.

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

Reason: the lines connecting the coordinates of both shapes meet at the origin. And also both figures are rectangles and all rectangles are similar (B)

the formula of a slope:

we have the points (-2, 7) and (2, 3). substitute:

10.4 inches

step-by-step explanation:

2x2x2.6