Question

A point is translated on the coordinate plane from (5,6) to (3,6). Peter writes the function f (x) = x + h to describe the translation. What is the value of h?

The value of h is ____.

Answer 1

To determine the value of \( h \) in the function \( f(x) = x + h \) for the translation from the point \( (5, 6) \) to the point \( (3, 6) \), we can start by focusing on the change in the \( x \)-coordinate.

Initially, the point is at \( (5, 6) \). After the translation, the \( x \)-coordinate becomes \( 3 \). This means the translation takes place in the \( x \)-direction.

We can represent this translation mathematically by finding out how much we need to adjust the \( x \)-coordinate from \( 5 \) to \( 3 \):

\[
3 = 5 + h
\]

To isolate \( h \), we can rearrange the equation:

\[
h = 3 - 5
\]
\[
h = -2
\]

Thus, the value of \( h \) is \( -2 \). The final answer is:

The value of \( h \) is \(-2\).