Question

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

a ( _, _ )
b ( _, _ )
c ( _, _ )

Explanation:

Step1: Recall reflection over x - axis rule

The rule for reflecting a point \((x,y)\) over the \(x\) - axis is \((x,-y)\).

Step2: Find \(A'\)

For point \(A(-4,2)\), using the reflection rule, \(x=-4\) and \(y = 2\). So the reflected point \(A'\) has coordinates \((-4,-2)\).

Step3: Find \(B'\)

For point \(B(4,7)\), using the reflection rule, \(x = 4\) and \(y=7\). So the reflected point \(B'\) has coordinates \((4,-7)\).

Step4: Find \(C'\)

For point \(C(5,1)\), using the reflection rule, \(x = 5\) and \(y = 1\). So the reflected point \(C'\) has coordinates \((5,-1)\).

Answer:

\(A'(-4,-2)\), \(B'(4,-7)\), \(C'(5,-1)\)