A 90^(∘) rotation counterclockwise about the origin will change the coordinates of the vertices such that (a,b)→ (- b,a).
Practice makes perfect
Let's begin by drawing △ LMN.
When a figure is rotated 90^(∘) counterclockwise about the origin, the coordinates of the image's vertices will change in the following way.
preimage (a,b)→ image (- b,a)
Using this rule on the vertices of △ LMN, we can find the coordinates of the rotated figure.
Point
(a,b)
(- b,a)
L
(1,6)
(- 6,1)
M
(- 2,4)
(- 4,- 2)
N
(3,2)
(- 2,3)
Now we can draw △ L'M'N'.
The second transformation is a translation of △ L'N'M' by 3 steps to the left and 2 steps up.
(x,y) → (x - 3,y + 2)
Let's perform these translations.
Finally, we will remove △ L'M'N' from the diagram.
