Reflection in the x-axis

Reflection in the x-axis

How to find the image under the reflection in the x-axis: formula, example, and its solution.

Formula

The image of a point (x, y) under the reflection in the x-axis is (x, -y).

The image of a point (x, y)
under the reflection in the x-axis is
(x, -y).

To find the image,
change the sign of the y value.

Example

Graph the given triangle and its image under the reflection in the x-axis on the coordinate plane. Triangle ABC with vertices A(-4, 2), B(5, 4), and C(3, 1)

To find the image
under the reflection in the x-axis,
change the sign of the y value.

The image of A(-4, 2) is
A'(-4, -2).

The image of B(5, 4) is,
change the sign of the y value,
B'(5, -4).

The image of C(3, -1) is,
change the sign of the y value,
C'(3, 1).

ABC has vertices
A(-4, 2), B(5, 4), and C(3, -1).

A'B'C' has vertices
A'(-4, -2), B'(5, -4), and C'(3, 1).

Use these vertices
to draw △ABC and its image △A'B'C'
on the coordinate plane.

As you can see,
A'B'C' is under the reflection in the x-axis.

The triangle is only filped.
There's no change in its size.

So, under a reflection,
not only in the x-axis,
the length and the area are reserved.