Question

the point z(4, -3) is reflected over the y-axis. what are the coordinates of the resulting point, z?

Explanation:

Step1: Recall reflection over y - axis rule

When a point \((x,y)\) is reflected over the \(y\) - axis, the \(y\) - coordinate remains the same and the \(x\) - coordinate changes its sign. The formula for the reflection of a point \((x,y)\) over the \(y\) - axis is \((x,y)\to(-x,y)\).

Step2: Apply the rule to point \(Z(4, - 3)\)

For the point \(Z(4,-3)\), here \(x = 4\) and \(y=-3\). Using the reflection rule over the \(y\) - axis, we substitute \(x = 4\) into \(-x\) and keep \(y=-3\) the same. So the new \(x\) - coordinate is \(-4\) and the \(y\) - coordinate is \(-3\).

Answer:

The coordinates of the resulting point \(Z'\) are \((-4,-3)\)