Finding Reflections Across the Axis of Symmetry

Learn how to find the reflections of given coordinate points across the vertical axis of symmetry x = -3 using horizontal distance formulas.

Answer

To find the reflection of a point across a vertical line

, the

-coordinate remains the same, and the new

-coordinate is found by ensuring the line

is the midpoint between the original

and the reflected

. The formula is

In this problem, the axis of symmetry is the vertical line

Reflection of :
Since the point lies exactly on the axis of symmetry , its reflection is itself.
Reflection of :
The -coordinate remains . The distance from to the axis is unit to the right. The reflected point will be unit to the left of the axis:
Reflection of :
The -coordinate remains . The distance from to the axis is units to the right. The reflected point will be units to the left of the axis:

The reflection of

.
The reflection of

Question