Question

(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

Answer 1

Answer: b

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

Answer 2

Answer:

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:

$\dfrac{EF}{AB}=\dfrac{EH}{AD}=\dfrac{FG}{BC}=\dfrac{HG}{DC}=\dfrac{4}{3}$

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 )