Question

If coordinates (-4, 7) undergo a translation vector of <-4,8> in the coordinate plane, what would the resulting coordinated be?

a. (-8, 15)
b. (-8, -1)
c. (8, -15)
d. (0, -1)

Answer 1

To find the resulting coordinates after applying the translation vector <-4, 8> to the original coordinates (-4, 7), we need to add the components of the translation vector to the corresponding components of the original coordinates.

The original coordinates are:
- \(x = -4\)
- \(y = 7\)

The translation vector components are:
- \(x\) component = -4
- \(y\) component = 8

Now, we calculate the new coordinates:
- New \(x\) coordinate:
\[
-4 + (-4) = -4 - 4 = -8
\]
- New \(y\) coordinate:
\[
7 + 8 = 15
\]

Therefore, the resulting coordinates after the translation are \((-8, 15)\).

The correct answer is:
**a. (-8, 15)**