Question

triangle abc with vertices a(-4, 2), b(4, 7), and c(5, 1): x - axis

Explanation:

Step1: Recall reflection rule

When reflecting a point $(x,y)$ over the $x - axis$, the rule is $(x,y)\to(x, - y)$.

Step2: Reflect point A

For point $A(-4,2)$, applying the rule gives $A'(-4,- 2)$.

Step3: Reflect point B

For point $B(4,7)$, applying the rule gives $B'(4,-7)$.

Step4: Reflect point C

For point $C(5,1)$, applying the rule gives $C'(5,-1)$.

Answer:

The vertices of the reflected triangle are $A'(-4,-2)$, $B'(4,-7)$, $C'(5,-1)$.