First translate the △ JKL one unit to the left and three units down and then rotate the image 90 ^(∘) about the origin O.
Practice makes perfect
The transformation (r_((90 ^(∘),O)) ∘ T_(<- 1,- 3>))(△JKL) means that △JKL will be translated one unit to the left and three units down and then the image will be rotated 90 ^(∘) about the origin O.
We will do these two things one at a time.
Translation
To move △ JLK one unit to the left and three units down, we have to subtract 1 from each x-coordinate and 3 from each y-coordinate.
(x,y) → (x-1,y-3)
Let's do it!
Rotation
Now we will rotate △JKL 90^(∘) about the origin. Unless we are told otherwise, we perform rotations counterclockwise. We will label the new image △J''K''L''.
Final Image
Finally, we will show the preimage △JKL and the image △J''K''L'' after the translation and the rotation.
