Question

give the coordinates of the point obtained from each reflection.
(a) reflect the point (4, -5) across the x-axis:
(b) reflect the point (4, -5) across the y-axis:

Explanation:

Step1: Reflect across the x - axis

When reflecting a point \((x,y)\) across the \(x\) - axis, the \(x\) - coordinate remains the same, and the \(y\) - coordinate changes its sign.
For the point \((4,-5)\), after reflection across the \(x\) - axis, the \(x\) - coordinate is \(4\) and the \(y\) - coordinate is \(-(-5)=5\).

Step2: Reflect across the y - axis

When reflecting a point \((x,y)\) across the \(y\) - axis, the \(y\) - coordinate remains the same, and the \(x\) - coordinate changes its sign.
For the point \((4,-5)\), after reflection across the \(y\) - axis, the \(x\) - coordinate is \(-4\) and the \(y\) - coordinate is \(-5\).

Answer:

(a) \((4,5)\)
(b) \((-4,-5)\)