Question

Which graph shows the dilation image of rectangle ABCD with the center of dilation at the origin and a scale factor of 1.5?

Answer 1

The correct graph will be the second option.

Explanation

Co ordinates of the original rectangle ABCD are : A(-6, 0) , B(0, 6) , C(6, 0) and D(0, -6)

Dilation at the origin with a scale factor means, we need to multiply both x and y co ordinates of each point by the scale factor.

Here, scale factor is given as 1.5

So, dilation points of A, B, C and D:

$A' = [(-6*1.5) , (0*1.5)] = (-9,0)\\ \\ B'= [(0*1.5),(6*1.5)]=(0,9)\\ \\ C'= [(6*1.5),(0*1.5)]=(9,0)\\ \\ D'= [(0*1.5),(-6*1.5)]=(0,-9)$

So, the correct graph will be the second option.