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What is the image point of left parenthesis, 4, comma, minus, 7, right parenthesis(4,−7) after a translation right 4 units and up 5 units?

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To find the image point of the point \((4, -7)\) after a translation 4 units to the right and 5 units up, we need to add 4 to the x-coordinate and 5 to the y-coordinate.

  1. Starting point: \((4, -7)\)
  2. Translate right 4 units: \[ 4 + 4 = 8 \]
  3. Translate up 5 units: \[ -7 + 5 = -2 \]

So, the new coordinates after the translation will be \((8, -2)\).

The final answer is: \[ (8, -2) \]