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.