Question

Quadrilateral ABCD is dilated with a scale factor of 2, with the center of dilation at the origin. The vertices of ABCD are A(0,0), B(5,0), C(5,3), and D(0,3). What are the coordinates of the image of Vertex C under the dilation?

Answer 1

Given a quadrilateral ABCD with vertices

A(0,0)

B(5,0)

C(5,3)

D(0,3)

The quadrilateral is as shown below:

When dilated with a scale factor of 2 at the origin, the coordinates of the vertices are multiplied by 2 to get a new image.

Thus, we have

$\begin{gathered} A(0,0)\Rightarrow A^{\prime}(0,0) \\ B(5,0)\Rightarrow B^{\prime}(10,0) \\ C(5,3)\Rightarrow C^{\prime}(10,6) \\ D(0,3)\Rightarrow D^{\prime}(0,6) \end{gathered}$

Thus, the coordinates of the image of vertex C is (10,6)