Question

which ordered pair represents a point on the perpendicular bisector of the segment shown? (3, 6) (1, 2) (3, 3) (2, 4) (2, 2)

Explanation:

Step1: Find mid - point of segment

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. For points $(1,2)$ and $(3,6)$, we have $x_1 = 1,y_1 = 2,x_2 = 3,y_2 = 6$. So the mid - point is $(\frac{1+3}{2},\frac{2 + 6}{2})=(2,4)$.

Step2: Recall property of perpendicular bisector

A point on the perpendicular bisector of a line segment is equidistant from the endpoints of the segment. The mid - point of a line segment lies on its perpendicular bisector.

Answer:

(2, 4)