C - Reflections Lesson

Reflections

In this module, we are going to explore different types of transformations: reflections, translations and rotations. All of these transformations preserve the shape of the object being transformed. This means that the shape will not get smaller or larger, it will just move around!

Reflecting an object creates a mirror image over a specific line of reflection. We will focus on three common lines of reflection: the y-axis, the x-axis and the line y=x.

Reflections
y-axis	x-axis	y = x

Notice, that when point A is reflected, it becomes A'. This is called "A prime" and it means the transformed point A.

Properties preserved when an object is reflected:
1. Distances: segment lengths do not change!
2. Angles: the angle measures do not change!
3. Parallel and perpendicular lines remain parallel and perpendicular!
4. Midpoints: midpoints of segments do not change!
When an object is reflected the ORIENTATION (order of letters) is reversed!

Let's review how the coordinates of a figure change with different reflections.

Reflections

y-axis

x-axis

y = x

graph of reflected triangle ABC over y-axis

graph of reflected triangle ABC over x-axis

graph of reflected triangle ABC over XY-axis

The x-coordinate takes the opposite sign, and the y-coordinate remains the same.

Ex: $LaTeX: B\left(-2,5\right)\longrightarrow B^1\left(2,5\right)$ $B\left(-2,5\right)\longrightarrow B^1\left(2,5\right)$

The y-coordinate takes the opposite sign, and the x-coordinate remains the same.

Ex: equation image indicator $LaTeX: B\left(-2,5\right)\longrightarrow B^1\left(-2,-5\right)$ $B\left(-2,5\right)\longrightarrow B^1\left(-2,-5\right)$

The x- and y-coordinates change places.

Ex: $LaTeX: B\left(-2,5\right)\longrightarrow B^1\left(5,-2\right)$ $B\left(-2,5\right)\longrightarrow B^1\left(5,-2\right)$

Try the problems below to see if you've got it!

Reflections Practice

IMAGES CREATED BY GAVS