Leap Year

Learning Focus

Find images of points and figures under reflections over axes, lines like $y=x$, and vertical lines.

Big idea

A reflection sends each point to the point the same distance on the opposite side of the mirror 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 a line $x=k$: $(x,y)\to(2k-x,\,y)$.

Worked example

Reflect $(1,3)$ over $x=4$.

The point is $3$ units left of the line, so the image is $3$ units right: $x=4+3=7$. Image: $(7,3)$.

Formula check: $2(4)-1=7$.

Takeaways

• Mirror line is the perpendicular bisector of each point and its image.
• Memorize the axes and $y=x$ rules.
• Use distance from the mirror for other lines.