User:

Dilations: find the coordinates

In a coordinate plane, dilations whose center are the origin have the property that the image of P(x,y) is P'(kx,ky) where k is the scale factor of the dilation.

Draw a dilation of rectangle ABCD with A(2,2), B(6,2), C(6,4), and D(2,4). Use the origin as the center and use a scale factor of $\frac{1}{2}$.

Because the center of the dilation is the origin, you can find the image of each vertex by multiplying its coordinates by the scale factor.

 A(2,2) $\rightarrow$ A'(1,1) B(6,2) $\rightarrow$ B'(3,1) C(6,4) $\rightarrow$ C'(6,2) D(2,4) $\rightarrow$ D'(1,2)

Graphycally:

Write the coordinates of the vertices after a dilation with a scale factor of 5, centered at the origin.

D(-1,-2) $\Rightarrow$ D*(,)
E(3,-2) $\Rightarrow$ E*(,)
F(1,3) $\Rightarrow$ F*(,)