Question

reflections find the coordinates
the point c(-5,-6) is reflected over the y-axis. what are the coordinates of the resulting point, c?
grid image showing point c and y-axis
options:
c(5,6)
c(5,-6)
c(-5,-6)
c(-5,6)

Explanation:

Step1: Recall reflection over y - axis rule

The rule for reflecting a point \((x,y)\) over the \(y\) - axis is that the \(x\) - coordinate changes its sign and the \(y\) - coordinate remains the same. Mathematically, if we have a point \(P(x,y)\), after reflection over the \(y\) - axis, the new point \(P'\) has coordinates \((-x,y)\).

Step2: Apply the rule to point \(C(-5,-6)\)

For the point \(C(-5,-6)\), where \(x=-5\) and \(y = - 6\). When we reflect over the \(y\) - axis, the new \(x\) - coordinate is \(-(-5)=5\) and the \(y\) - coordinate remains \(-6\). So the coordinates of \(C'\) are \((5,-6)\).

Answer:

\(C'(5,-6)\)