Question

1. triangle abc has vertices a(-5,6), b(1,-2), and c(-3,-4). what are the coordinates of the vertices of △abc for each reflection?

a. r_{x - axis}

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 \(A(-5,6)\)

For point \(A(-5,6)\), using the rule \((x,y)\to(x, - y)\), we get \(A'(-5,-6)\) since \(x=-5\) and \(y = 6\) (so \(-y=-6\)).

Step3: Apply the rule to point \(B(1,-2)\)

For point \(B(1,-2)\), using the rule \((x,y)\to(x, - y)\), we get \(B'(1,2)\) since \(x = 1\) and \(y=-2\) (so \(-y = 2\)).

Step4: Apply the rule to point \(C(-3,-4)\)

For point \(C(-3,-4)\), using the rule \((x,y)\to(x, - y)\), we get \(C'(-3,4)\) since \(x=-3\) and \(y =-4\) (so \(-y = 4\)).

Answer:

\(A'(-5,-6)\), \(B'(1,2)\), \(C'(-3,4)\)