18.1 Reflection, rotation and translation — Practise with help

1. $5$. Starting at $-3$ and moving $8$ places right gives $5$.
2. $24$. Multiply $4$ by $6$.

Change the sign of the coordinate perpendicular to the mirror line.

The $y$-axis is vertical, so keep $y=-2$ and change $x=4$ to $-4$.

Image $(-4,-2)$. The point and image have equal distances from the $y$-axis.

Use $(x,y)\mapsto(-y,x)$.

Substitute $x=3$ and $y=1$ to get $(-1,3)$.

The image is $(-1,3)$ after a quarter-turn anticlockwise.

Use the inverse operation.

Divide both sides by $3$.

$x=6$.