Question

△jkl is rotated 90° about the origin and then translated using (x, y)→(x - 8,y + 3). what are the coordinates of the final image of point l under this composition of transformations? (-12, 5) (-2, -12) (-9, 7) (-7, -6)

Explanation:

Step1: Identify initial coordinates of point L

The coordinates of point L from the graph are $(4, - 1)$.

Step2: Apply 90 - degree rotation about the origin

The rule for a 90 - degree counter - clockwise rotation about the origin is $(x,y)\to(-y,x)$. For point L$(4,-1)$, after rotation, the new coordinates are $(1,4)$.

Step3: Apply the translation

The translation rule is $(x,y)\to(x - 8,y + 3)$. For the point $(1,4)$ after rotation, we substitute $x = 1$ and $y = 4$ into the translation rule.
$x'=1-8=-7$
$y'=4 + 3=7$

Answer:

$(-7,7)$

It seems there is an error in the provided options as the correct answer $(-7,7)$ is not among them.