Question

#8: point a is shown on the graph below. what are the coordinates of point a after a reflection over the x - axis? what is the distance between the original point and its reflection?

Explanation:

Step1: Determine the original coordinates of point A

From the graph, the coordinates of point A are \((2,-3)\).

Step2: Find the coordinates after reflection over the x - axis

When a point \((x,y)\) is reflected over the x - axis, the rule is \((x,y)\to(x, - y)\).
For point \(A(2,-3)\), after reflection over the x - axis, the new coordinates are \((2,3)\).

Step3: Calculate the distance between the original point and its reflection

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
Here, \(x_1 = 2,y_1=-3,x_2 = 2,y_2 = 3\).
Substitute into the formula:

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Answer:

The coordinates of point A after reflection over the x - axis are \((2,3)\) and the distance between the original point and its reflection is \(6\).