Reflection in the Origin

Reflection in the Origin

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

Formula

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

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

To find the image,
change the signs of both x and y values.

Example

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

To find the image
under the reflection in the origin,
change the signs of both x and y values.

The image of A(-3, 5) is
A'(3, -5).

The image of B(5, 4) is,
change the signs of both x and y values,
B'(-5, -4).

The image of C(2, -1) is,
change the signs of both x and y values,
C'(-2, 1).

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

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

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

So, under a reflection,
not only in the origin,
the length and the area are reserved.