Reflections: How to reflect a point

Reflect point across x axis, y axis and other lines

A reflection is a kind of transformation. It is basically a 'flip' of a shape over the line of reflection.

Very often reflecions are performed using coordinate notation as they all are on this page. The coordinates allow us to easily describe the image and its preimage.

Examples

of the most common types of

Reflections in Math

Reflection in the x-axis

A reflection in the x-axis can be seen in the picture below in which A is reflected to its image A'.

The general rule for a reflection in the x-axis: (A,B) (A, −B)

picture of reflection in the y-axis

Reflection in the y-axis

A reflection in the y-axis can be seen in the picture below in which A is reflected to its image A'.

The general rule for a reflection in the y-axis: (A,B) (−A, B)

picture of reflection in the x-axis

Reflection in the line y = x

A reflection in the line y = x can be seen in the picture below in which A is reflected to its image A'.

The general rule for a reflection in the y-axis: (A, B) (B, A)

picture of reflection in the line y=x

Practice Problems

Perform the reflections indicated below

Problem 1

What is the image of point A(1,2) after reflecting it across the x-axis . In technical speak, pefrom the following transformation r(x-axis)?

Picture of reflection across y axis
Problem 2

What is the image of point A (31,1) after reflecting it across the x-axis . In technical speak, pefrom the following transformation r(y-axis)?

Picture of reflection across y axis
Problem 3

What is the image of point A(-2,,1) after reflecting it across the the line y = x . In technical speak, pefrom the following transformation r(y=x)?

Picture of reflection across y axis