Question

Find the component form of the vector that translates p(-3, 6) To P’(-4, 8)

Answer 1

To find the component form of the vector that translates point \( P(-3, 6) \) to point \( P'(-4, 8) \), we can use the formula:

\[
\text{Vector} = P' - P
\]

This means we will subtract the coordinates of \( P \) from the coordinates of \( P' \) component-wise.

1. For the x-component:
\[
-4 - (-3) = -4 + 3 = -1
\]

2. For the y-component:
\[
8 - 6 = 2
\]

Thus, the component form of the vector is:

\[
\mathbf{v} = \langle -1, 2 \rangle
\]

So the vector that translates \( P(-3, 6) \) to \( P'(-4, 8) \) is \( \langle -1, 2 \rangle \).