Question

If coordinates (−2,−5) undergo a translation vector of <2,−3> in the coordinate plane, what would the resulting coordinates be?

Answer 1

To determine the resulting coordinates after applying the translation vector \(\langle 2, -3 \rangle\) to the point \((-2, -5)\), you will add the components of the translation vector to the coordinates of the point.

1. Start with the original coordinates: \((-2, -5)\).
2. Add the x-component of the translation vector (which is \(2\)) to the x-coordinate:
\[
-2 + 2 = 0
\]
3. Add the y-component of the translation vector (which is \(-3\)) to the y-coordinate:
\[
-5 + (-3) = -8
\]

Putting it all together, the new coordinates after the translation are:
\[
(0, -8)
\]

Thus, the resulting coordinates are \(\boxed{(0, -8)}\).