Question

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

Explanation:

Step1: Determine the original coordinates of point S

From the graph, the coordinates of point S are \((-5,4)\).

Step2: Apply the reflection rule over the y - axis

The rule for reflecting a point \((x,y)\) over the y - axis is \((-x,y)\).
For the point \((-5,4)\), after reflection, \(x=-(-5) = 5\) and \(y = 4\). So the reflected point \(S'\) has coordinates \((5,4)\).

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, \((x_1,y_1)=(-5,4)\) and \((x_2,y_2)=(5,4)\).
Substitute into the formula: \(d=\sqrt{(5-(-5))^2+(4 - 4)^2}=\sqrt{(5 + 5)^2+0^2}=\sqrt{10^2}=10\).

Answer:

The coordinates of the reflected point are \((5,4)\) and the distance between the original point and its reflection is \(10\).