Translation Coordinates Eb313E

1. **Problem:** Translate a figure 8 units left and 7 units up and find the new coordinates. 2. **Formula for translation:** If a point has coordinates $ (x, y) $, after translation by $a$ units horizontally and $b$ units vertically, the new coordinates are $$ (x', y') = (x + a, y + b) $$ 3. **Important rules:** - Moving left means subtracting from the $x$-coordinate. - Moving right means adding to the $x$-coordinate. - Moving up means adding to the $y$-coordinate. - Moving down means subtracting from the $y$-coordinate. 4. **Apply translation 8 units left and 7 units up:** - Left 8 units means $a = -8$ - Up 7 units means $b = +7$ 5. **New coordinates:** $$ (x', y') = (x - 8, y + 7) $$ 6. **Explanation:** Each point of the original figure moves 8 units to the left (subtract 8 from $x$) and 7 units up (add 7 to $y$). --- For the other translations mentioned: - Translation (0, 4) means $a=0$, $b=4$, so new coordinates are $$ (x', y') = (x, y + 4) $$ - Translation $ (x, y) \to (x + 6, y) $ means $a=6$, $b=0$, so new coordinates are $$ (x', y') = (x + 6, y) $$ **Final answer for the first translation:** $$ \boxed{(x', y') = (x - 8, y + 7)} $$