Question

△abc has vertices a(2,2), b(2,5), and c(4,2). name the coordinates of the image of point c after each transformation.

1. reflect △abc in the x - axis, and then reflect that image in the y - axis.

c(□,□)

Explanation:

Step1: Reflect over the x - axis

When reflecting a point \((x,y)\) over the \(x\) - axis, the rule is \((x,y)\to(x, - y)\).
For point \(C(4,2)\), after reflection over the \(x\) - axis, the new \(y\) - coordinate is \(-2\), and the \(x\) - coordinate remains the same. So the image is \(C_1(4,- 2)\).

Step2: Reflect over the y - axis

When reflecting a point \((x,y)\) over the \(y\) - axis, the rule is \((x,y)\to(-x,y)\).
For point \(C_1(4,-2)\), after reflection over the \(y\) - axis, the new \(x\) - coordinate is \(-4\), and the \(y\) - coordinate remains the same.

Answer:

\((-4,-2)\)