Question

The shape ABCD shown below has to be dilated about Vertex A by a scale factor of 2, the new position of Vertex C will be.

• A. (150,100)
• B. (150,200)
• C. (250,150)
• D. (250,200)

Answer 1

The correct option is C (250,150)

Initial position of Vertex C = (150,100)

Horizintal distance between A and C on x-axis = 150 - 50 = 100 units

Vertical distance between A and C on y-axis = 100 - 50 = 50 units

Since the image is dilated by a scale factor of 2, the distance between A and C increases by 2 times along the axes w.r.t. A.

Hence, the new position of C w.r.t. distance from A = 100 $\times$ 2 = 200 along x-axis and 50 $\times$ 2 along y-axis

So, the new shape A${}_1$B${}_1$C${}_1$D${}_1$ is,
Here, the new Vertex C has coordinates (250, 150).