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

# How to Reflect a Shape in the Line y = -x

To reflect a shape in the line**y = -x**, for each vertex (corner) of the shape:

**Step 1:**Find the diagonal distance to the line

**y = -x**.

**Step 2:**Draw the reflected vertex the same diagonal distance on the other side of the line

**y = -x**.

When all vertices have been reflected, draw the reflected shape.

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

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

**y = -x**.

- For point
**A**:

**Step 1:**Find the diagonal distance to the line**y = -x**.

Point**A**is 1½ diagonals from the line**y = -x**.

**Step 2:**Draw the reflected vertex the same distance on the other side of the line**y = -x**.

- For point
**B**:

**Step 1:**Find the diagonal distance to the line**y = -x**.

Point**B**is ½ a diagonal from the line**y = -x**.

**Step 2:**Draw the reflected vertex the same distance on the other side of the line**y = -x**.

- For point
**C**:

**Step 1:**Find the diagonal distance to the line**y = -x**.

Point**C**is 2½ diagonals from the line**y = -x**.

**Step 2:**Draw the reflected vertex the same distance on the other side of the line**y = -x**.

This is the shape reflected in the line

**y = -x**.

# How to Reflect a Shape in the Line y = -x Using Cartesian Co-ordinates

In the above example, the shape has been reflected by reading off visually the distance of points from the line**y = -x**.

An alternative method transforms the Cartesian co-ordinates of each point

**(x, y)**to its reflected point

**(-y, -x)**.

Read more about how to reflect a shape in the line y =-x using Cartesian co-ordinates

##### Curriculum

##### Interactive Test

**show**

##### Note

**WHAT IS A REFLECTION?**

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

By reflection, think of the reflection you would see in a mirror or in water. The orginal shape is called the object, the reflected shape is called the image:

It is as if the shape has been flipped.

A reflection is a type of transformation.

**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 top left to bottom right.

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

**y = -x**is at 45° to both axes.

##### Top Tip

**YOU DON'T HAVE TO MEASURE DIAGONALLY TO THE LINE**

In the real example, the diagonal distance of each vertex to the line is measured.

The reflected vertex is drawn the same diagonal distance on the other side of the line:

However, the measurement does not have to be diagonal. You can measure horizontally or vertically:

- Measure the
**vertical**distance to the line**y = -x**:

The reflected vertex is the same**horizontal**distance from**y = -x**:

- Measure the
**horizontal**distance to the line**y = -x**:

The reflected vertex is the same**vertical**distance from**y = -x**:

- diagonally
- vertical then horizontal
- horizontal then vertical