Question

which ordered pair represents a point on the perpendicular bisector of the segment shown? (4,5) (2,1) (2,4) (2,2) (3,3)

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 $(2,1)$ and $(4,5)$, we have $x_1=2,y_1 = 1,x_2=4,y_2 = 5$. Then the mid - point is $(\frac{2 + 4}{2},\frac{1+5}{2})=(3,3)$.

Step2: Recall property of perpendicular bisector

A point on the perpendicular bisector of a line segment is the mid - point of the segment or equidistant from the two endpoints of the segment. The mid - point of the given segment is $(3,3)$.

Answer:

(3, 3)