Reflections

A reflection is a transformation that flips a figure across a line, called the . The original figure and its are mirror images: every point moves to the opposite side of the line, the same distance away.

Reflecting over the axes

Make a prediction: The point (3, 1) is reflected over the y-axis. Where does its image land?

(−3, 1)(3, −1)(−3, −1)(1, 3)

Reflecting a point over the x-axis keeps its $x$ -coordinate and negates its $y$ -coordinate:

(x, y) \mapsto (x, -y)

Reflecting over the y-axis does the opposite — it negates the $x$ -coordinate and keeps $y$ :

(x, y) \mapsto (-x, y)

Because a reflection preserves distances and angles, the image is to the original. So a segment $\overline{AB}$ and its image $\overline{A'B'}$ always have the same length.

Switch the axis of reflection and watch where each vertex lands.

Reflect over

A triangle ABC reflected across the y-axis → triangle A′B′C′.

Practice

Score: 0/2

1.Reflecting the point (3, 2) over the x-axis gives which point?
(3, -2)(-3, 2)(2, 3)(-3, -2)
2.Reflect the point (5, 1) over the y-axis. What is the new x-coordinate?
Answer

For teachers

Standard, common misconceptions, and suggested use will live here.