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Point

\[P'\] is the image of
\[P(5,-5)\] under a translation by
\[2\] units to the left and
\[5\] units up.
What are the coordinates of
\[P'\]?

1 answer

To find the coordinates of the point \( P' \) after applying the translation to the point \( P(5, -5) \), we need to follow the given translation instructions: moving \( 2 \) units to the left and \( 5 \) units up.

  1. Translation to the left: Moving \( 2 \) units to the left means we subtract \( 2 \) from the x-coordinate. \[ x' = 5 - 2 = 3 \]

  2. Translation up: Moving \( 5 \) units up means we add \( 5 \) to the y-coordinate. \[ y' = -5 + 5 = 0 \]

Now, combining these results, the new coordinates of the point \( P' \) are: \[ P'(3, 0) \]

Thus, the coordinates of \( P' \) are \( \boxed{(3, 0)} \).