We are given the coordinates of polygon WXYZ and we want to find its image after a dilation. The first step will be graph WXYZ with the given vertices: W(8,-2), X(6,0), Y(-6,4), and Z(-2,2).
A dilation can be an enlargement, a reduction, or the same size as the preimage. Which type of dilation it is depends on the value of the scale factor k.
Enlargement
k>1
Reduction
0
Same
k=1
When the center of dilation in the coordinate plane is the origin, each coordinate of the preimage is multiplied by the scale factor k to find the coordinates of the image.
ccc
Preimage & & Image [0.5em]
(x,y)& ⇒ & ( kx, ky)
Now, let's find the coordinates of the vertices of ABC after a dilation with a scale factor k= - 0.5.
ccccc
(x,y) &→& ( -0.5x, -0.5y) &→& (x',y') [0.8em]
W(8,-2) &→& ( -0.5(8), -0.5(-2)) &→& W'(-4,1) [0.8em]
X(6,0) &→& ( -0.5(6), -0.5(0)) &→& X'(-3,0) [0.8em]
Y(-6,4) &→& ( -0.5(-6), -0.5(4)) &→& Y'(3,-2) [0.8em]
Z(-2,2) &→& ( -0.5(-2), -0.5(2)) &→& Z'(1,-1) [0.8em]
With the vertices of the image, we can graph the image in the same coordinate plane as the preimage.
