How to Reflect a Shape in the X-Axis Using Cartesian Coordinates

To reflect a shape in the x-axis using Cartesian coordinates, if a point on the shape has coordinates (x,y), the reflected point has coordinates (x,-y).

Method of How to Reflect a Point in the X-Axis Using Cartesian Coordinates

For each vertex (corner) of the shape:

Step 1: Find the Cartesian coordinate of the vertex.
(x,y)

Step 2: Find the Cartesian coordinate of the reflected vertex by changing the sign of the y co-ordinate.
(x,-y)

A Real Example of How to Reflect a Shape in the X-Axis Using Cartesian Coordinates

Question: Reflect the shape below in the x-axis.

Step 1: Find the Cartesian coordinates of each vertex.

Vertex of Object Coordinate
A (2,3)
B (5,2)
C (2,1)

Step 2: Find the Cartesian coordinate of the reflected vertex by changing the sign of the y co-ordinate.

Vertex of Object Coordinate Vertex of Image Co-ordinate
A (2,3) A' (2,-3)
B (5,2) B' (5,-2)
C (2,1) C' (2,-1)

With all the vertices reflected, we can draw in the reflected shape:

This is the shape reflected in the x-axis.
Geometry Lessons
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Note
FINDING THE CARTESIAN COORDINATES OF A POINT

• The coordinate on the left is the x-coordinate.

It describes how far along the x-axis, or how far across, the point is.

• The coordinate on the right is the y-coordinate.

It describes how far up the y-axis, or how far up, the point is.
For example, the point below is 2 along the x-axis and 3 up the y-axis. Therefore its Cartesian coordinates are (2,3)

WHAT IS A REFLECTION?

A reflection transforms a shape so that it becomes a mirror image of itself.

The orginal shape is called the object, the reflected shape is called the image.

A reflection is a type of transformation.