1. **Convert the vector \(\langle -3,1 \rangle\) into coordinate notation:** The vector is already in coordinate notation as \(\langle x,y \rangle\). So the coordinate notation is simply \((-3,1)\). 2. **Convert the vector \(\langle 4,-7 \rangle\) into coordinate notation:** Similarly, the vector is \(\langle 4,-7 \rangle\), so the coordinate notation is \((4,-7)\). 3. **Translate triangle JKL by the rule \((x,y) \to (x - 4, y + 1)\):** - Point \(J(2,4)\) translates to \(J'(2 - 4, 4 + 1) = (-2,5)\). - Point \(K(6,8)\) translates to \(K'(6 - 4, 8 + 1) = (2,9)\). - Point \(L(8,2)\) translates to \(L'(8 - 4, 2 + 1) = (4,3)\). **Coordinate for \(L'\) is \((4,3)\).** 4. **Translate triangle PRQ by the rule \((x,y) \to (x + 5, y - 3)\):** - Point \(P(-5,0)\) translates to \(P'(-5 + 5, 0 - 3) = (0,-3)\). - Point \(Q(1,6)\) translates to \(Q'(1 + 5, 6 - 3) = (6,3)\). - Point \(R(-6,-6)\) translates to \(R'(-6 + 5, -6 - 3) = (-1,-9)\). **Coordinate for \(R'\) is \((-1,-9)\).**