Question

state what transformation occurred?

1. a (-3, 2) b (5, 7) c (-8, 12)

a (3, -2) b (-5, -7) c(8, -12)

Explanation:

Compare each original point $(x,y)$ to its image $(x',y')$:

• For $A(-3,2)\to A'(3,-2)$: $x$-coordinate is negated, $y$-coordinate is negated
• For $B(5,7)\to B'(-5,-7)$: $x$-coordinate is negated, $y$-coordinate is negated
• For $C(-8,12)\to C'(8,-12)$: $x$-coordinate is negated, $y$-coordinate is negated

This matches the transformation rule for a rotation of $180^\circ$ about the origin, which is $(x,y)\to(-x,-y)$.

Answer:

A $180^\circ$ rotation about the origin (or the transformation $(x,y)\to(-x,-y)$)