Let's mark the given coordinates and graph the figure.
To find the coordinates of the image after a dilation with a scale factor of k, we multiply each coordinate of the preimage by k.
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.
Dilation With Scale Factor k=3
Preimage
Multiply by k
Image
A(- 3,1)
( 3(- 3), 3(1))
A'(- 9,3)
B(0,2)
( 3(0), 3(2))
B'(0,6)
C(2, - 2)
( 3(2), 3(- 2))
C'(6,- 6)
We can now plot the obtained points and connect them with segments to draw the image.
Checking Our Answer
To check our answer, we can draw rays from the origin through the vertices of the original figure. The vertices of the dilation should lie on those rays.
