We are given the coordinates of triangle LMN and we want to find its image after a dilation. The first step will be graph â–³ LMN with the given vertices: L(0,0), M(-4,1), and N(-3,-6).
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= - 3.
ccccc
(x,y) &→& ( -3x, -3y) &→& (x',y') [0.8em]
L(0,0) &→& ( -3(0), -3(0)) &→& L'(0,0) [0.8em]
M(-4,1) &→& ( -3(-4), -3(1)) &→& M'(12,-3) [0.8em]
N(-3,-6) &→& ( -3(-3), -3(-6)) &→& N'(9,18) [0.8em]
With the vertices of the image, we can graph the image in the same coordinate plane as the preimage.
