# How to Reflect a Shape In the Line y = x Using Cartesian Coordinates (Mathematics Lesson)

# How to Reflect a Shape in the Line y = x Using Cartesian Coordinates

To reflect a shape in the line**y = x**using Cartesian coordinates, if a point on the shape has coordinates

**(x,y)**, the reflected point has coordinates

**(y,x)**.

# Method of How to Reflect a Point in Line y = x 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 swapping the x-coordinate and the y-coordinate around.

**(y,x)**

# A Real Example of How to Reflect a Shape in the Line y = x Using Cartesian Coordinates

**Question:**Reflect the shape below in the line

**y = x**.

**Step 1:**Find the Cartesian coordinates of each vertex.

Vertex of Object | Coordinate |
---|---|

A |
(1,6) |

B |
(4,5) |

C |
(1,4) |

**Step 2:**Find the Cartesian coordinate of the reflected vertex by swapping the x-coordinate and the y-coordinate around.

Vertex of Object | Coordinate | Vertex of Image | Coordinate |
---|---|---|---|

A |
(1,6) |
A' |
(6,1) |

B |
(4,5) |
B' |
(5,4) |

C |
(1,4) |
C' |
(4,1) |

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

This is the shape reflected in the line

**y = x**.

##### Curriculum

##### Interactive Test

**show**

##### 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.

**2**along the x-axis and

**3**up the y-axis. Therefore its Cartesian coordinates are

**(2,3)**

**WHAT IS THE LINE y = x**

**y = x**is a linear equation.

**y = x**represents a diagonal line that goes through the origin. It goes from bottom left to top right.

It goes halfway between the x-axis and the y-axis.

**y = x**is at 45° to both axes.

**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.