Question

which coordinate pair shows the location of the image after ( m(3,-2) ) is reflected in the line ( y = 5 )?
o a) ( (3,3) )
o b) ( (3,12) )
o c) ( (7,-2) )
o d) ( (8,-2) )

Explanation:

Step1: Calculate the distance between the y - coordinate of the point and the line \(y = 5\)

The formula for the distance \(d\) between a point \((x,y)\) and the line \(y = k\) is \(d=\vert y - k\vert\).
For the point \(M(3,- 2)\) and the line \(y = 5\), \(d=\vert-2 - 5\vert=\vert-7\vert = 7\).

Step2: Find the y - coordinate of the reflected point

When a point \((x,y)\) is reflected over the line \(y = k\), the x - coordinate remains the same (\(x'=x\)), and the y - coordinate is \(y'=k+(k - y)\).
Since \(x = 3\), \(k = 5\) and \(y=-2\), then \(y'=5+(5-(-2))=5 + 7=12\).

Answer:

B. \((3,12)\)