Question

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

Explanation:

Step1: Find the distance between the y - coordinate of the point and the line of reflection

The line of reflection is \(y = 5\) and the y - coordinate of the point \(M(3,-2)\) is \(y=-2\). The distance \(d\) between \(y=-2\) and \(y = 5\) is \(d=\vert5-(-2)\vert=\vert5 + 2\vert=7\).

Step2: Calculate the y - coordinate of the reflected point

Since we are reflecting over a horizontal line \(y = 5\), the x - coordinate of the point remains the same (\(x = 3\)). To find the y - coordinate of the reflected point, we move the same distance \(d = 7\) above the line \(y = 5\). So the y - coordinate \(y=5 + 7=12\).

Answer:

B. \((3,12)\)