We are given the coordinates of triangle PQR and we want to find its image after a dilation. The first step will be graph â–ł BCD with the given vertices: B(-5,-10), C(-10,15), and D(0,5).
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= - 15.
ccccc
(x,y) &→& ( -1/5x, -1/5y) &→& (x',y') [1em]
B(-5,-10) &→& ( -1/5(-5), -1/5(-10)) &→& B'(1,2) [1em]
C(-10,15) &→& ( -1/5(-10), -1/5(15)) &→& C'(2,-3) [1em]
D(0,5) &→& ( -1/5(0), -1/5(5)) &→& D'(0,-1) [1em]
With the vertices of the image, we can graph the image in the same coordinate plane as the preimage.
