Let's start by graphing â–ł ABC. We have been given the points A(0,5), B(-10,-5), and C(5,-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 our scale factor. In our case k=120 %, so we will multiply by k= 1.2.
ccccc
(x,y) &→& ( 1.2x, 1.2y) &→& (x',y') [0.5em]
A(0,5) &→& ( 1.2(0), 1.2(5)) &→& A'(0,6) [0.8em]
B(-10,-5) &→& ( 1.2(-10), 1.2(-5)) &→& B'(-12,-6) [0.8em]
C(5,-5) &→& ( 1.2(5), 1.2(-5)) &→& C'(6,-6) [0.8em]
Now that we have calculated the points for the image, we can graph them in the same coordinate system as the preimage.
