16.3 - Reflections

Links and useful resources

Concept summary and connections

the image when we reflect point $A$ over line $m$ is the point $A^{'}$ such that $m$ is the perpendicular bisector of $\overset{―}{A A^{'}}$ . In other words, if we folded our paper along line $m$ , $A$ and $A^{'}$ would coincide.
If a figure maps to itself under a reflection over a certain line, that line is called a line of symmetry of the figure. For example, every diameter of a circle is part of a line of symmetry of a circle, and each diagonal of a square is part of a line of symmetry of the square.

Lesson and worked examples

A reflection is a transformation that "flips" a figure over an axis. If you draw the axis, then every part of the figure is transformed to make the axis be the midpoint between the new image and the old.

A diagram can be reflected even if the axis goes through it!

When the reflection of a diagram concides with the original diagram, then the reflection line is called a line of symmetry. A figure can have many lines of symmetry (or even infinite lines).

Guided practice

What are the fixed points of a reflection over a given line $m$ ? In other words, what points are their own images when reflected over line $m$ ?
Given two different points, $X$ and $Y$ , describe all lines $m$ such that the image of $X$ upon reflection over $m$ is point $Y$ .
How many different lines of symmetry does a regular hexagon have?
I own a cabin in the woods that is 4 miles directly north of a river that runs east-west. I am currently out exploring the woods. I am 2 miles north of the river, and 3 miles west and 2 miles south of my cabin. I want to walk to the river, then walk to the cabin. What is the length of the shortest possible route I can take?

Homework

#hw (geom-gr10) 16.3 Reflections (p. 413) (gr10) 2025-03-31