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C = (-5,1)

Jarvis wants to translate rectangle ABDC horizontally by −4 and vertically by +3 to produce rectangle A′B′D′C′. What will be the coordinates of C′ after Jarvis completes this translation?

1 answer

To translate the point \( C = (-5, 1) \) horizontally by \(-4\) and vertically by \(+3\), we can apply the translation to the coordinates of point \( C \).

  1. Horizontal translation:

    • Move \( C \) horizontally by \(-4\): \[ x' = -5 + (-4) = -5 - 4 = -9 \]

  2. Vertical translation:

    • Move \( C \) vertically by \(+3\): \[ y' = 1 + 3 = 4 \]

Now, combining these translations, the new coordinates \( C' \) will be: \[ C' = (-9, 4) \]

Thus, the coordinates of \( C' \) after the translation are \(\boxed{(-9, 4)}\).