Question

identify a point on the perpendicular bisector to $overline{cb}$ on the graph. (4,3) (5,0) (6,1)

Explanation:

Step1: Find mid - point of $\overline{CB}$

The coordinates of $C$ seem to be $(1,2)$ and of $B$ seem to be $(9,2)$. The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. So, for $C(1,2)$ and $B(9,2)$, the mid - point $M$ is $(\frac{1 + 9}{2},\frac{2+2}{2})=(5,2)$.

Step2: Analyze perpendicular bisector

The line segment $\overline{CB}$ is a horizontal line ($y = 2$). The perpendicular bisector of a horizontal line is a vertical line passing through its mid - point. The equation of the perpendicular bisector of $\overline{CB}$ is $x = 5$.

Step3: Check given points

Among the points $(4,3)$, $(5,0)$ and $(6,1)$, the point with $x = 5$ is $(5,0)$.

Answer:

$(5,0)$