Let's start by graphing â–ł XYZ. We have been given the points X(6,-1), Y(-2,-4), and Z(1,2).
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') [0.5em]
X(6,-1) &→& ( 3(6), 3(-1)) &→& X'(18,-3) [0.8em]
Y(-2,-4) &→& ( 3(-2), 3(-4)) &→& Y'(-6,-12) [0.8em]
Z(1,2) &→& ( 3(1), 3(2)) &→& Z'(3,6) [0.8em]
Now that we have calculated the points for the image, we can graph them in the same coordinate system as the preimage.
