Integrated Math 1 / Unit 8: Transformations and Congruence
8.3 Reflections
Notes
A reflection flips a figure over a line of reflection, creating a mirror image.
- Over the $x$-axis: $(x, y) \to (x, -y)$. Over the $y$-axis: $(x, y) \to (-x, y)$. Over $y = x$: $(x, y) \to (y, x)$.
- Each point and its image are the same distance from the line, on opposite sides, and the segment joining them is perpendicular to the line.
- A reflection reverses orientation (clockwise order becomes counterclockwise).
- Example: reflect $(4, 3)$ over the line $x = 1$: the point is 3 units right of the line, so the image is 3 units left, at $(-2, 3)$.
Practice
What is the image of $(3, -2)$ reflected over the $x$-axis?
Reflecting over the $x$-axis changes the sign of $y$.
What is the image of $(2, 7)$ reflected over the line $y = x$?
Reflection over $y = x$ swaps the coordinates.
Point $(4, 3)$ is reflected over the vertical line $x = 1$. What is the image?
The point is 3 units right of $x = 1$, so the image is 3 units left of it, at $x = -2$.
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