To perform the rotation, we can use the coordinate rule. When a figure is rotated 90^(∘) counterclockwise about the origin, the coordinates of the figure's vertices change such that (a,b)→ (- b,a).
ccc
(a,b) & → & (- b,a) [0.5em]
F(- 2,2) & → & F'(- 2,- 2)
G(-2,-4) & → & G'(4,-2)
H(-4,-4) & → & H'(4,-4)
Now we are able to graph △ F'G'H'.
Dilation
Next, we will dilate △ F'G'H' using a scale factor of 3. To do this, we need to multiply the coordinates by 3.
ccccc
(x,y) &→& (3x,3y) &→& (x',y') [0.8em]
F'(-2,-2) &→& (3(-2),3(-2)) &→& F''(-6,-6) [0.8em]
G'(4,-2) &→& (3(4),3(-2)) &→& G''(12,-6) [0.8em]
H'(4,-4) &→& (3(4),3(-4)) &→& H''(12,-12)
Now, we can show the dilation by plotting the newly obtained points.
Combined Transformation
Finally, we can remove the middle step and only look at the preimage and the image.
