Question

right triangle lmn has vertices l(7, -3), m(7, -8), and n(10, -8). the triangle is translated on the coordinate plane so the coordinates of l are (-1, 8). which rule was used to translate the image? (x, y) → (x + 6, y - 5) (x, y) → (x - 6, y + 5) (x, y) → (x + 8, y - 11) (x, y) → (x - 8, y + 11)

Explanation:

Step1: Analyze x - coordinate change

The original x - coordinate of L is 7, and the new x - coordinate of L' is - 1. Calculate the change in x: $7-(-1)=8$, so the x - coordinate changes by subtracting 8, i.e., $x\to x - 8$.

Step2: Analyze y - coordinate change

The original y - coordinate of L is - 3, and the new y - coordinate of L' is 8. Calculate the change in y: $8-(-3)=11$, so the y - coordinate changes by adding 11, i.e., $y\to y + 11$.
So the translation rule is $(x,y)\to(x - 8,y + 11)$.

Answer:

D. $(x,y)\to(x - 8,y + 11)$