Question

in the coordinate plane, the points ( a(1,9) ), ( b(5,-11) ), and ( c(-7,-10) ) are reflected over the ( x )-axis to the points ( a ), ( b ), and ( c ), respectively. what are the coordinates of ( a ), ( b ), and ( c )?

Explanation:

Step1: Recall the reflection rule over the x - axis

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

Step2: Apply the rule to point \(A(1,9)\)

For \(A(1,9)\), using the rule \((x,y)\to(x, - y)\), we get \(A'(1,-9)\).

Step3: Apply the rule to point \(B(5, - 11)\)

For \(B(5,-11)\), using the rule \((x,y)\to(x, - y)\), we get \(B'(5,11)\).

Step4: Apply the rule to point \(C(-7,-10)\)

For \(C(-7,-10)\), using the rule \((x,y)\to(x, - y)\), we get \(C'(-7,10)\).

Answer:

\(A'(1,-9)\), \(B'(5,11)\), \(C'(-7,10)\)