Drawing and reflecting shapes on the coordinate grid

​​In a nutshell

You will look at moving shapes by reflection in the $$x$$ or $$y$$ axis. Like a mirror, a reflection will flip the position of an object to the opposite side. Therefore, to reflect points or shapes, you will be learning to use all four quadrants.

Reflection in the $$x$$ axis​

The $$x$$ axis is the horizontal axis on the coordinate plane. It can be written as the line $$y = 0$$.​

Example 1

Reflect the triangle $$ABC$$ in the $$x$$ axis. Identify the new coordinates. 

$$\underline{A':(3,-2)}$$​​

$$\underline{B':(5,-5)}$$​​

$$\underline{C':(7,-2)}$$​​

Note: Sometimes shapes will look different after being reflected.

Reflection in the $$y$$ axis

The $$y$$ axis is the vertical axis on the coordinate plane. It can be written as the line $$x = 0$$.

Example 2

Reflect parallelogram one in the $$y$$ axis.

Note: Each corner should be an equal distance from the line of reflection; in this case this is the $$y$$​ axis.

Multiple-step reflections

You may be asked to reflect a shape multiple times. The order you reflect a shape is very important to determine its final position. 

Example 3

In the coordinate plane below, reflect square one in the line $$x=0$$ followed by the line $$y=0$$. 

Note: First you reflect the square in the $$y$$ axis, then the $$x$$ axis.