The green triangle is a dilation of the red triangle with a scale factor of s=13 and the center of dilation is at the point (4,2) What are the coordinates of Point C'? C'(___,_)

What are the coordinates of Point A? A(_,_)

Given:

The red figure dilated with a scale factor of and the center of dilation is at the point (4,2) to get the green figure.

To find:

The coordinates of C' and A.

Solution:

If a figure is dilated with a scale factor k and the center of dilation is at the point (a,b), then

In given problem, the scale factor is and the center of dilation is at (4,2).

           ...(i)

Let the vertices of red triangle are A(m,n), B(10,14) and C(-2,11).

Using (i), we get

Therefore, the coordinates of Point C' are C'(2,5).

We assumed that point A is A(m,n).

Using (i), we get

From the given figure it is clear that the image of point A is (8,4).

On comparing both sides, we get

And,

Therefore, the coordinates of point A are (16,8).