Quadrilateral ABCD has vertices A(–1, –2), B(–1, 3), C(4, 3) and D(4, –2). It's dilated by a factor of 2 with the center of dilation at the origin. What are the coordinates of the resulting quadrilateral A'B'C'D'?

Given:

Quadrilateral ABCD has vertices A(–1, –2), B(–1, 3), C(4, 3) and D(4, –2).

It's dilated by a factor of 2 with the center of dilation at the origin.

To find:

The coordinates of the resulting quadrilateral A'B'C'D'.

Solution:

The figure dilated by a factor of 2 with the center of dilation at the origin. So, the rule of dilation is

Using the above rule, we get

Therefore, the coordinates of the resulting quadrilateral A'B'C'D' are A'(-2,-4), B'(-2,6), C'(8,6) and D'(8,-4).

point a is the center of this circle.

the ratio of the lengths of (ef/bc) and (ad/ih) is 2: 1.

step-by-step explanation: