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 the change in x - coordinate

The original x - coordinate of \(L\) is \(x = 7\), and the new x - coordinate of \(L'\) is \(x'=-1\).
We use the formula \(x'=x + a\), where \(a\) is the horizontal translation. Substituting the values: \(-1=7 + a\), then \(a=-1 - 7=-8\).

Step2: Analyze the change in y - coordinate

The original y - coordinate of \(L\) is \(y=-3\), and the new y - coordinate of \(L'\) is \(y' = 8\).
We use the formula \(y'=y + b\), where \(b\) is the vertical translation. Substituting the values: \(8=-3 + b\), then \(b=8+ 3 = 11\).

Answer:

\((x,y)\to(x - 8,y + 11)\)