Question

What are the coordinates of point (-4,3)
after it is reflected across the line x=−2
?

Answer 1

To reflect a point across a vertical line, we need to determine how far the point is from the line and then move it the same distance on the opposite side of the line.

The line of reflection is \(x = -2\). The original point is \((-4, 3)\).

1. Find the horizontal distance from the point to the line:
- The x-coordinate of the point is \(-4\).
- The x-coordinate of the line is \(-2\).
- The distance from the point to the line is:
\[
\text{Distance} = -4 - (-2) = -4 + 2 = -2
\]
This means the point is 2 units to the left of the line.

2. To reflect the point, we move it 2 units to the right of the line:
- Starting from the line \(x = -2\), moving 2 units to the right gives us:
\[
-2 + 2 = 0
\]

3. The y-coordinate remains unchanged during the reflection since we are reflecting over a vertical line:
- The y-coordinate of the original point is \(3\).

Thus, the coordinates of the point \((-4, 3)\) after reflecting across the line \(x = -2\) are \((0, 3)\).