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

## Reflecting a Shape in y = x Using Cartesian Coordinates

A shape can be reflected in the line y = x.

If point on a shape is reflected in the line y = x, the x-coordinate becomes the y-coordinate and the y-coordinate becomes the x-coordinate.

The image below shows a point on a shape being reflected in the line y = x: • The point A has Cartesian coordinates (2, 3).

• The reflected point A' has Cartesian coordinates (3, 2).

The x-coordinate of A (2) has become the y-coordinate of A'. The y-coordinate of A (3) has become the x-coordinate of A'.

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

Reflecting a shape in the line y = x using Cartesian coordinates is easy.

### Question

Reflect the shape below in the line y = x. # 1

Find the Cartesian coordinates of each point on the shape.

Write the x-coordinates and y-coordinates of each point.

Point x-coordinate y-coordinate
A 1 6
B 4 5
C 1 4

# 2

Find the Cartesian coordinates of the reflected points.

Swap the x-coordinate and the y-coordinate of the original point.

Point x-coordinate y-coordinate Point x-coordinate y-coordinate
A 1 6 A' 6 1
B 4 5 B' 5 4
C 1 4 C' 4 1

# 3

Plot the reflected points and draw in the shape.

We have reflected the shape in the line y = x. ## A Formula to Reflect a Point in y = x Using Cartesian Coordinates

In general, we write Cartesian coordinates as: x is the x-coordinate. y is the y-coordinate. x and y can taken any number.

The reflected point has Cartesian coordinates: The image below shows a general Cartesian coordinate being reflected in the line y = x: ## Slider

The slider below shows another real example of how to reflect a shape in the line y = x using Cartesian coordinates.

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