When a figure is rotated 90^(∘) counterclockwise about the origin, the coordinates of the image's endpoints will change in the following way.
(a,b)→ (- b,a)
Graph:
Does it matter?: Yes
Practice makes perfect
Let's graph RS as well as the ghosts of R'S' and R''S'' when we do the reflection first followed by the rotation.
Let's switch it around and start by doing a rotation of 90^(∘) about the origin. When a figure is rotated 90^(∘) counterclockwise about the origin, the coordinates of the image's endpoints will change in the following way:
(a,b)→ (- b,a).
Using this rule on the endpoints of RS, we can find the endpoints of R'S',
Point
(a,b)
(- b,a)
R
(1,- 3)
(3,1)
S
(2,- 6)
(6,2)
Now we can graph R'S'
Finally, we perform the reflection in the y-axis which changes the coordinates of the preimage in the following way
(a,b) → (- a,b)
Using this rule on the endpoints of R'S', we can find the endpoints of R''S''.
Point
(a,b)
(- a,b)
R'
(3,1)
(- 3,1)
S'
(6,2)
(- 6,2)
Now we can graph R''S''.
As we can see, it does matter which order you perform the transformations.
