Reflection

A reflection is a type of transformation. To reflect a shape you need to know the mirror line (line of reflection).

For each vertex of the shape:

1. Measure the perpendicular distance from the point to the mirror line.
2. Plot the image point the same distance on the other side.

Common mirror lines on a coordinate grid include:

• The $x$-axis (the line $y = 0$)
• The $y$-axis (the line $x = 0$)
• The line $y = x$
• The line $y = -x$

When reflecting in the $y$-axis, the $x$-coordinate changes sign: $(x, y) \to (-x, y)$.
When reflecting in the $x$-axis, the $y$-coordinate changes sign: $(x, y) \to (x, -y)$.

Explore: reflection

Choose a mirror line and press Transform to see the reflected image. Press Reset to start again.

Watch it work

Question: Reflect the point $A(3, 2)$ in the $y$-axis. State the coordinates of the image.

Have a go