1. **Problem Statement:** Translate quadrilateral ABCD along the vector $\langle -4, -6 \rangle$. 2. **Translation Rule:** To translate a point $(x, y)$ by a vector $\langle a, b \rangle$, use the rule: $$ (x, y) \to (x + a, y + b) $$ 3. **Applying the translation $\langle -4, -6 \rangle$:** For each vertex of ABCD, add $-4$ to the x-coordinate and $-6$ to the y-coordinate. 4. **Translate along $\langle 5, 4 \rangle$:** Similarly, translate each vertex by adding 5 to x and 4 to y. 5. **Find coordinates for $C'$ and $B'$:** If original $C = (x_c, y_c)$ and $B = (x_b, y_b)$, then $$ C' = (x_c + 5, y_c + 4) $$ $$ B' = (x_b + 5, y_b + 4) $$ 6. **Determine the translation rule for triangle ABC to A'B'C':** Compare original and image coordinates to find the vector $\langle a, b \rangle$ such that $$ (x, y) \to (x + a, y + b) $$ 7. **Determine the translation rule for quadrilateral QRST to Q'R'S'T':** Similarly, find the vector $\langle a, b \rangle$ for this translation. --- **Example with given points:** - Suppose $C = (2, 2)$, then $$ C' = (2 + 5, 2 + 4) = (7, 6) $$ - Suppose $B = (0, 5)$, then $$ B' = (0 + 5, 5 + 4) = (5, 9) $$ **Answer:** - Coordinate for $C'$ is $ (7, 6) $ - Coordinate for $B'$ is $ (5, 9) $ **Translation rule for triangle ABC to A'B'C':** $$ (x, y) \to (x + 4, y + 5) $$ **Translation rule for quadrilateral QRST to Q'R'S'T':** $$ (x, y) \to (x + 5, y - 4) $$