Question

the image of (2, 8) under a translation is (-3, 10). find the image of (-3, 7) under the same translation.

Explanation:

Step1: Find the translation vector

Let the translation vector be \((h, k)\). For a point \((x, y)\), its image under translation is \((x + h, y + k)\). Given the original point \((2, 8)\) and its image \((-3, 10)\), we have:
\(2 + h = -3\) and \(8 + k = 10\)
Solving for \(h\): \(h = -3 - 2 = -5\)
Solving for \(k\): \(k = 10 - 8 = 2\)
So the translation vector is \((-5, 2)\).

Step2: Apply the translation to \((-3, 7)\)

Now, apply the translation vector \((-5, 2)\) to the point \((-3, 7)\).
For the \(x\)-coordinate: \(-3 + (-5) = -8\)
For the \(y\)-coordinate: \(7 + 2 = 9\)

Answer:

\((-8, 9)\)