When a figure is rotated 90^(∘) counterclockwise about the origin, the coordinates of the figure's endpoints change such that (x,y)→ (- y,x).
Using this rule with the endpoints of CD, we can find the endpoints of C'D'.
ccc
(x,y) & → & (- y,x) [0.5em]
C(- 2,2) & → & C'(- 2,- 2)
D(2,2) & → & D'(- 2,2)
Now we are able to graph C'D'. Let's do it!
Dilation
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 endpoints of C'D' after a dilation with a scale factor k= 12.
Dilation With Scale Factor k= 12
Preimage
Multiply by k
Image
C'(- 2,- 2)
( 12 (- 2), 12 (- 2))
C''(- 1,- 1)
D'(- 2,2)
( 12 (- 2), 12 (2))
D''(- 1,1)
Now, we can show the transformation by plotting the newly obtained points.
Combined Transformation
Finally, we can remove the middle step and only look at the preimage and the image.
