Question

give the coordinates of the point obtained from each reflection.
(a) reflect the point (7, 0) across the y-axis.
(□, □)
(b) reflect the point (7, 0) across the x-axis.
(□, □)

Explanation:

Part (a)

Step1: Recall reflection over y - axis rule

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

Step2: Apply the rule to the point \((7,0)\)

For the point \((7,0)\), where \(x = 7\) and \(y=0\), when we reflect it across the \(y\) - axis, we change the sign of the \(x\) - coordinate. So the new \(x\) - coordinate is \(- 7\) and the \(y\) - coordinate remains \(0\). So the reflected point is \((-7,0)\).

Part (b)

Step1: Recall reflection over x - axis rule

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

Step2: Apply the rule to the point \((7,0)\)

For the point \((7,0)\), where \(x = 7\) and \(y = 0\), when we reflect it across the \(x\) - axis, we change the sign of the \(y\) - coordinate. Since \(y = 0\), \(-y=0\). So the reflected point is \((7,0)\).

Answer:

(a) \((-7,0)\)
(b) \((7,0)\)