Question

triangle lmn is shifted according to the translation shown in the table. find the coordinates for each vertex of triangle lmn.

triangle lmn	translation	triangle lmn
l $(2, -3)$		l $(square, square)$
m $(1, -2)$		m $(square, square)$
n $(-4, 1)$		n $(square, square)$

Explanation:

Step1: Find L' coordinates

For point L(2, -3), apply translation \((x - 3, y + 2)\).
\(x\)-coordinate: \(2 - 3 = -1\)
\(y\)-coordinate: \(-3 + 2 = -1\)
So L' is \((-1, -1)\).

Step2: Find M' coordinates

For point M(1, -2), apply translation \((x - 3, y + 2)\).
\(x\)-coordinate: \(1 - 3 = -2\)
\(y\)-coordinate: \(-2 + 2 = 0\)
So M' is \((-2, 0)\).

Step3: Find N' coordinates

For point N(-4, 1), apply translation \((x - 3, y + 2)\).
\(x\)-coordinate: \(-4 - 3 = -7\)
\(y\)-coordinate: \(1 + 2 = 3\)
So N' is \((-7, 3)\).

Answer:

L' \((-1, -1)\)
M' \((-2, 0)\)
N' \((-7, 3)\)