Question

given a(5, -2), what are the coordinates of the image of a after a reflection across the x-axis?
a. (-2, 5)
b. (-5, 2)
c. (-5, -2)
d. (5, 2)

Explanation:

Step1: Recall reflection over x - axis rule

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

Step2: Apply the rule to point \(A(5,-2)\)

For the point \(A(5,-2)\), the \(x\) - coordinate is \(x = 5\) and the \(y\) - coordinate is \(y=-2\). Using the reflection rule across the \(x\) - axis, the new \(x\) - coordinate will still be \(5\), and the new \(y\) - coordinate will be \(-y=-(-2) = 2\). So the coordinates of the image of \(A\) after reflection across the \(x\) - axis are \((5,2)\).

Answer:

D. \((5, 2)\)