To dilate the figure, let's start by graphing â–ˇ JKLM. We have been given the points J(4,0), K(-8,4), L(0,-4), and M(12,-8).
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= 0.25.
ccccc
(x,y) &→& ( 0.25x, 0.25y) &→& (x',y') [0.8em]
J(4,0) &→& ( 0.25(4), 0.25(0)) &→& J'(1,0) [0.8em]
K(-8,4) &→& ( 0.25(-8), 0.25(4)) &→& K'(-2,1) [0.8em]
L(0,-4) &→& ( 0.25(0), 0.25(-4)) &→& L'(0,-1) [0.8em]
M(12,-8) &→& ( 0.25(12), 0.25(-8)) &→& M'(3,-2) [0.8em]
Now that we have calculated the points for the image, we can graph them in the same coordinate system as the preimage.
