The green triangle is a dilation of the red triangle with a scale factor of s=1/3 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 scale factor is and the center of dilation is at the point (4,2).

Red is original figure and green is dilated figure.

To find:

The coordinates of point C' and point A.

Solution:

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

According to the given information, the scale factor is and the center of dilation is at (4,2).

           ...(i)

Let us assume 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).