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:

Scale factor

Center of dilation = (4,2)

To find:

The coordinates of the points C' and A.

Solution:

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

The scale factor is and the center of dilation is at (4,2).

           ...(i)

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

Using rule (i), we get

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

Let us assume that point A is A(m,n).

Using rule (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).