Given a scale factor of 1/2, find the coordinates for the dilation of the triangle with vertices at (0, 0), (0, 2), (4,0)

Given: A scale factor of .

Let centre of dilation at origin.

As we can see that the vertices of the triangle at (0,0), (0,2) and (4,0) forms a right triangle.    

Dilation states that the transformation that produces an image that is the same shape as the original, but of a different size.

The rule for Dilation  is where k is the scale factor i.e,

or we can write the rule as :

Multiply the each coordinates of the triangle by , to find the coordinates for the dilation of the triangle.

(0,0)

(0,2) = (0,1)

and (4,0) = (2,0)

Therefore, the coordinate after the dilation are (0,0) , (0,1) and (2,0).

We plot a graph for both the triangle in coordinate plane: