Question

A point is translated on the coordinate plane from (4, -1) to (6, -1). which function shows this translation.

Answer 1

To define the translation from the point \((4, -1)\) to \((6, -1)\), we first need to identify the change in the x-coordinates, as the y-coordinate remains unchanged.

1. The x-coordinate changes from \(4\) to \(6\), which is an increase of \(2\) units.
2. The y-coordinate remains constant at \(-1\).

Therefore, the point can be translated using a translation function that reflects this change. In general, a translation in the coordinate plane can be represented as:

\[
T(x, y) = (x + a, y + b)
\]

Where \((a, b)\) represents the translation vector. In this case:

- \(a = 2\) (the change in x)
- \(b = 0\) (the change in y)

Putting this into the translation function, we have:

\[
T(x, y) = (x + 2, y)
\]

So the function that shows the translation from the point \((4, -1)\) to \((6, -1)\) is:

\[
T(x, y) = (x + 2, y)
\]