Reflection in the y-axis

Reflection in the y-axis

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

Formula

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

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

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

Example

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

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

The image of A(-2, 1) is
A'(2, 1).

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

The image of C(3, -2) is,
change the sign of the x value,
C'(-3, -2).

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

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

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 y-axis.

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

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