Question

Rectangle ABCD has vertices A(4, 8), B(8, 8) , C(8, −4) and D(4, −4) . The rectangle is dilated by a scale factor of 3/4 , with the origin as the center of dilation. What are the coordinates of the vertices in the image? Enter your answers in the boxes.

Answer 1

Answer:

A'(3, 6)

B'(6, 6)

C'(6, -3)

D'(3, -3)

Step-by-step explanation:

To find the image of a geometric figure after a dilation centered at the origin, you just need to multiply each vertex of the geometric figure by the scale factor.

We know that the scale factor is $\frac{3}{4}$, so let's multiply each vertex by it:

$A=(4, 8)$, so

$A'=\frac{3}{4} (4,8)=(\frac{3}{4} *4,\frac{3}{4} *8)=(3,6)$

$B=(8,8)$

$B'=(\frac{3}{4} *8,\frac{3}{4} *8)=(6,6)$

$C=(8,-4)$

$C'=(\frac{3}{4} *8,\frac{3}{4} *-4)=(6, -3)$

$D=(4,-4)$

$D'=(\frac{3}{4} *4,\frac{3}{4} *-4)=(3,-3)$

We can conclude that the vertices of the image are A'(3, 6), B'(6, 6), C'(6, -3), and D'(3, -3)