Let's start by graphing â–ˇ TUVW. We have been given the points T(9,-3), U(6,0), V(3,9), and W(0,0).
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= 23.
ccccc
(x,y) &→& ( 2/3x, 2/3y) &→& (x',y') [1em]
T(9,-3) &→& ( 2/3(9), 2/3(-3)) &→& T'(6,-2) [1em]
U(6,0) &→& ( 2/3(6), 2/3(0)) &→& U'(4,0) [1em]
V(3,9) &→& ( 2/3(3), 2/3(9)) &→& V'(2,6) [1em]
W(0,0) &→& ( 2/3(0), 2/3(0)) &→& W'(0,0) [1em]
Now that we have calculated the points for the image, we can graph them in the same coordinate system as the preimage.
