Question

Find the component form of the vector that translates p(-3, 6) to P’(0,1)

Answer 1

To find the component form of the vector that translates the point \( P(-3, 6) \) to the point \( P'(0, 1) \), we need to determine the change in the x-coordinates and the change in the y-coordinates.

The vector \( \vec{v} \) that translates \( P \) to \( P' \) can be found using the formula:

\[
\vec{v} = (x' - x, y' - y)
\]

where \( (x, y) \) are the coordinates of point \( P \) and \( (x', y') \) are the coordinates of point \( P' \).

Plugging in the coordinates:

- \( P = (-3, 6) \)
- \( P' = (0, 1) \)

We calculate:

1. Change in x: \( x' - x = 0 - (-3) = 0 + 3 = 3 \)
2. Change in y: \( y' - y = 1 - 6 = -5 \)

Thus, the component form of the vector is:

\[
\vec{v} = (3, -5)
\]

This means that the vector that translates the point \( P(-3, 6) \) to \( P'(0, 1) \) is \( \vec{v} = (3, -5) \).