Question

c. (7, -2) d. (2, -7) a. reflection over the x-axis changes the coordinates of the point (4,6) to: a. (-4, -6) b. (-4,6) c. (4, -6) d. (4,6)

Explanation:

Step1: Recall reflection over x - axis rule

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

Step2: Apply the rule to the point \((4,6)\)

For the point \((4,6)\), where \(x = 4\) and \(y=6\), when we reflect it over the \(x\) - axis, the \(x\) - coordinate \(x = 4\) stays the same, and the \(y\) - coordinate \(y = 6\) changes to \(-y=-6\). So the reflected point is \((4,-6)\).

Answer:

c. \((4, - 6)\)