Coordinate Plane:

Reflections

6th Grade Math

Hernandez

Plot the following points

• Plot the following points:

• Figure 1: (-2, 2) (-5,2) (-2,7)

• Figure 2: (2,2) (5,2) (2,7)

• Connect the dots of each figure

What do you notice about these figures

They are Mirror images of one another

• We can say that they are reflected over the y−axis because the y−axis is

acting like a mirror for the two triangles.

• We call this the line of reflection, because the y−axis is doing the

reflecting. Imagine standing in front of a mirror and holding up your left

hand.

• Where is your hand in the mirror’s reflection? A reflected figure works the

same way: when we flip it over the line of reflection, all of its points are

reversed.

• We can reflect an image over the x−axis or over the y−axis.

Do you see any patterns?

If you look carefully, you will see that

the x−coordinates of the reflected triangle are

opposite those of the first triangle.

This is a rule to help you.

Reflections over the x-axis

• Plot the following points and connect the dots

• (2, 1)

• (7, 1)

• (6, 3)

• (3, 3)

What are the new points?

• What do you know about reflecting over the y- axis?

• What point changes? What point stays the same?

• Plot the new points over the x- axis

How’d you do?

Rule: Y coordinate changes to its opposite when you are reflecting over the X-Axis

Reflected points over the x-axis:

• (2, -1)

• (7, -1)

• (3, -3)

• (6, -3)

Reflected Image

You can see that the x−axis forms a line of reflection so that one trapezoid becomes the mirror image of the other

trapezoid

.

Throughout this lesson you have learned how to reflect figures on the coordinate plane.

When this happens, we can see a mirror of two figures.

We reflected figures over the x−axis and over the y−axis.

Sometimes, a figure will have parts that mirror themselves within one object.

In this case, parts of the object match other parts of the picture.

This is called symmetry. Let’s look at examples .

A Heart

Butterflies