Question

question
the image of the point (-9,9) under a translation is (-5,13). find the coordinates of the image of the point (-6,-7) under the same translation.
answer attempt 1 out of 2
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Explanation:

Step1: Find the translation vector

Let the translation vector be \((h, k)\). For the point \((-9, 9)\) translated to \((-5, 13)\), we use the formula:
New \(x\)-coordinate = Original \(x\)-coordinate + \(h\)
New \(y\)-coordinate = Original \(y\)-coordinate + \(k\)

For \(x\)-coordinate: \(-5 = -9 + h\), so \(h = -5 - (-9) = 4\)
For \(y\)-coordinate: \(13 = 9 + k\), so \(k = 13 - 9 = 4\)
The translation vector is \((4, 4)\).

Step2: Apply the translation to \((-6, -7)\)

Using the translation vector \((4, 4)\) on the point \((-6, -7)\):
New \(x\)-coordinate: \(-6 + 4 = -2\)
New \(y\)-coordinate: \(-7 + 4 = -3\)

Answer:

\((-2, -3)\)