Leaping Lizards!

Learning Focus

Describe translations, reflections, and rotations as rigid motions that preserve length and angle measure.

Big idea

A rigid motion moves a figure without changing its size or shape.

• Translation: slide by $(x,y)\to(x+a,y+b)$.
• Reflection: flip over a line.
• Rotation: turn about a point by an angle.
• Rigid motions preserve distance and angle measure. A dilation does not.

Worked example

Translate $A(3,-2)$ by $(x,y)\to(x+4,y+5)$.

$A'=(3+4,\,-2+5)=(7,3)$.

If segment $AB$ has length $7$, then $A'B'=7$. If $\angle A=52^\circ$, then $\angle A'=52^\circ$.

Takeaways

• Rigid motions keep lengths and angles.
• Translations, reflections, rotations are rigid; dilations are not.
• Image points are labeled with primes.