Question

the figure below has a point marked with a large dot. first, reflect the figure across the y-axis. then, give the coordinates of the marked point in the original figure and the final figure. point in original figure: point in final figure: question 12 of 20 give the coordinates of the point obtained from each reflection. (a) reflect the point (5, 0) across the x-axis. (b) reflect the point (5, 0) across the y-axis. (a) reflect the point (5, 0) across the x-axis. ( , ) (b) reflect the point (5, 0) 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 \((5,0)\)

For the point \((5,0)\), where \(x = 5\) and \(y=0\), when we reflect across the \(x\) - axis, we substitute into the rule. So the new \(x\) - coordinate is \(5\) and the new \(y\) - coordinate is \(- 0=0\).

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 \((5,0)\)

For the point \((5,0)\), where \(x = 5\) and \(y = 0\), when we reflect across the \(y\) - axis, we substitute into the rule. So the new \(x\) - coordinate is \(-5\) and the new \(y\) - coordinate is \(0\).

Answer:

(a) \((5,0)\)
(b) \((- 5,0)\)