Question

reflections find the coordinates
the point o(-6,4) is reflected over the y-axis. what are the coordinates of the resulting point, o?
image of coordinate grid with point o and y-axis
o(-6, -4) o(6, 4)
o(-6, 4) o(6, -4)

Explanation:

Step1: Recall reflection over y - axis rule

When a point \((x,y)\) is reflected over the \(y\) - axis, the rule 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 the given point

The given point is \(O(-6,4)\). Here, \(x=-6\) and \(y = 4\). Using the reflection over \(y\) - axis rule, the \(x\) - coordinate of the reflected point \(O'\) will be \(-(-6)=6\) and the \(y\) - coordinate will remain \(4\). So the coordinates of \(O'\) are \((6,4)\).

Answer:

\(O'(6,4)\)