Question

give the coordinates of the point obtained from each reflection.
(a) reflect the point (-9, -6) across the x-axis: (□, □)
(b) reflect the point (-9, -6) across the y-axis: (□, □)

Explanation:

Part (a)

Step1: Recall reflection over x - axis rule

The rule for reflecting a point \((x,y)\) across the \(x\) - axis is \((x,-y)\).

Step2: Apply the rule to the point \((-9,-6)\)

Here, \(x=-9\) and \(y = - 6\). So, when we reflect across the \(x\) - axis, the new \(y\) - coordinate is \(-y=-(-6) = 6\) and the \(x\) - coordinate remains the same. So the reflected point is \((-9,6)\).

Part (b)

Step1: Recall reflection over y - axis rule

The rule for reflecting a point \((x,y)\) across the \(y\) - axis is \((-x,y)\).

Step2: Apply the rule to the point \((-9,-6)\)

Here, \(x = - 9\) and \(y=-6\). So, when we reflect across the \(y\) - axis, the new \(x\) - coordinate is \(-x=-(-9)=9\) and the \(y\) - coordinate remains the same. So the reflected point is \((9,-6)\).

Answer:

(a) \((-9, 6)\)
(b) \((9, -6)\)