Start by drawing AB and plotting the given points on a coordinate grid.
C
Practice makes perfect
We are asked which of the given points lies on the perpendicular bisector of AB. Let's start with a diagram.
We can see above that neither (3,12), nor (1,5), nor (3,3) are on the perpendicular bisector of AB. Hence, the only point which might be on the perpendicular bisector of AB is (6,6). To determine so, let's recall the Converse of the Perpendicular Bisector Theorem.
Converse of the Perpendicular Bisector Theorem
If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment.
Therefore, to determine if (6,6) is on the perpendicular bisector of AB, we will find the distance to the endpoints of AB. To do so, we will use the Distance Formula.
d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)
Let's find the distance between A(1,3) and (6,6) by substituting (1,3) and (6,6) for (x_1,y_1) and (x_2,y_2) in the above formula.
We found that the distance between A(1,3) and (6,6) is sqrt(34). Let's now find the distance between B(1,9) and (6,6) using substitution one more time.
We found that the distance between B(1,9) and (6,6) is also sqrt(34). Therefore, (6,6) is equidistant from the endpoints of AB and thus it is on the perpendicular bisector of AB. Hence the correct choice is C.
