Geometry / Unit 4: Transformations
4.2 Reflections
Notes
A reflection flips a figure over a line, the line of reflection. Each point and its image are the same distance from the line.
- Over the $x$-axis: $(x, y) \to (x, -y)$.
- Over the $y$-axis: $(x, y) \to (-x, y)$.
- Over $y = x$: $(x, y) \to (y, x)$. Over $y = -x$: $(x, y) \to (-y, -x)$.
- Reflections are rigid motions, but they reverse orientation (clockwise becomes counterclockwise).
- Example: reflecting $(3, -5)$ over the $y$-axis gives $(-3, -5)$.
Practice
Reflect $(2, 7)$ over the $x$-axis.
Over the $x$-axis, keep $x$ and negate $y$.
Reflect $(-4, 1)$ over the line $y = x$.
Over $y = x$, swap the coordinates.
Reflect $(5, 2)$ over the vertical line $x = 3$.
$(5, 2)$ is 2 units right of $x = 3$, so its image is 2 units left, at $x = 1$.
Ready for more? Take the Unit 4 test.