Question

give the coordinates of the point obtained from each reflection.
(a) reflect the point $(3, -6)$ across the $y$-axis:
(b) reflect the point $(3, -6)$ across the $x$-axis:

Explanation:

Step1: Reflect across y - axis

When reflecting a point \((x,y)\) across the \(y\) - axis, the rule is \((x,y)\to(-x,y)\).
For the point \((3,-6)\), we change the sign of the \(x\) - coordinate. So, \(x = 3\) becomes \(-3\) and \(y=-6\) remains the same. The new point is \((-3,-6)\).

Step2: Reflect across x - axis

When reflecting a point \((x,y)\) across the \(x\) - axis, the rule is \((x,y)\to(x,-y)\).
For the point \((3,-6)\), we change the sign of the \(y\) - coordinate. So, \(x = 3\) remains the same and \(y=-6\) becomes \(6\). The new point is \((3,6)\).

Answer:

(a) \((-3,-6)\)
(b) \((3,6)\)