Question

what points are 3 units away from (-2, -2) with the same y coordinate?

Answer 1

To find the points that are 3 units away from the point \((-2, -2)\) with the same \(y\) coordinate, we need to keep the \(y\) coordinate fixed at \(-2\) and vary the \(x\) coordinate.

The distance formula for points on a horizontal line (where \(y\) is constant) can be simplified. If we denote the new point as \((x, -2)\), the distance from \((-2, -2)\) to \((x, -2)\) must equal 3 units. Thus, we can set up the equation:

\[
|x - (-2)| = 3
\]

This simplifies to:

\[
|x + 2| = 3
\]

This absolute value equation gives us two cases to consider:

1. \(x + 2 = 3\)
2. \(x + 2 = -3\)

Now, we'll solve each case:

1. From \(x + 2 = 3\):
\[
x = 3 - 2 = 1
\]

2. From \(x + 2 = -3\):
\[
x = -3 - 2 = -5
\]

Thus, the points that are 3 units away from \((-2, -2)\) with the same \(y\) coordinate are:

\[
(1, -2) \quad \text{and} \quad (-5, -2)
\]