We are given the coordinates of polygon RSTU and we want to find its image after a dilation. The first step will be graph RSTU with the given vertices: R(-7,-1), S(2,5), T(-2,-3), and U(-3,-3).
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= - 4.
ccccc
(x,y) &→& ( -4x, -4y) &→& (x',y') [0.8em]
R(-7,-1) &→& ( -4(-7), -4(-1)) &→& R'(28,4) [0.8em]
S(2,5) &→& ( -4(2), -4(5)) &→& S'(-8,-20) [0.8em]
T(-2,-3) &→& ( -4(-2), -4(-3)) &→& T'(8,12) [0.8em]
U(-3,-3) &→& ( -4(-3), -4(-3)) &→& U'(12,12) [0.8em]
With the vertices of the image, we can graph the image in the same coordinate plane as the preimage.
