Question

Find the co-ordinates of the point at which the perpendicular bisector of the line segment joining the points (1,5) and (4,6) cuts the y-axis.

Answer:

The co-ordinates of the point are (0,13).

P and Q are the given points. CD is the perpendicular bisector of PQ and C is the midpoint of PQ. We have to find the co-ordinates of D.
The slope of the line PQ is (6-5/4-1) = 1/3. As CD and PQ are perpendicular to each other the product of their slopes will be equal to -1. Therefore, slope of line CD = -3.
The co-ordinates of C are (5/2,11/2) [By the section formula]
Therefore, we have the equation:
(11/2-y)/(5/2-0) = -3 which implies (11-2y)/5 = -3 which further implies 11-2y = -15 which implies that 2y = 26 and thus, we get y = 13.
Therefore, the co-ordinates of the required point is (0,13).


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