Question

a triangle has vertices at ( a(-7,3) ), ( b(2,6) ), and ( c(3,5) ). what are the coordinates of each vertex if the triangle is reflected over the ( x )-axis?
( a(7,-3), b(-2,-6), h(-3,-5) )
( a(-7,3), b(-2,6), h(-3,-5) )
( a(-7,-3), b(2,-6), c(3,-5) )
( a(7,3), b(-2,6), h(-3,5) )

Explanation:

Step1: Recall the rule for reflection 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 \(A(-7,3)\)

For point \(A(-7,3)\), using the rule \((x,y)\to(x, - y)\), we get \(A'(-7,- 3)\).

Step3: Apply the rule to point \(B(2,6)\)

For point \(B(2,6)\), using the rule \((x,y)\to(x, - y)\), we get \(B'(2,-6)\).

Step4: Apply the rule to point \(C(3,5)\)

For point \(C(3,5)\), using the rule \((x,y)\to(x, - y)\), we get \(C'(3,-5)\).

Answer:

\(A'(-7,-3),B'(2,-6),C'(3,-5)\) (the third option in the given choices)