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# Points A and B have coordinates (7, – 3) and (1, 9) respectively. Find (i) the slope of AB. (ii) the equation of the perpendicular bisector of the line segment AB. (iii) the value of ‘p’ if ( – 2, p) lies on it.

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This question is Based on Equation of a Straight Line Chapter of M.L Aggarwal book for ICSE BOARD for class 10.
Here co-ordinates of two point are given, Find the slope , the equation of the perpendicular bisector of the line segment AB.
This is the Question Number 35, Exercise 12.2 of M.L Aggarwal.

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1. Given, co-ordinates of points A are (7, -3) and of B are (1, 9)

(i) The slope of AB (m) = (9 + 3)/ (1 – 7) = 12/ (-6) = -2

(ii) Let PQ be the perpendicular bisector of AB intersecting it at M

Now, the co-ordinates of M will be the mid-point of AB

Co-ordinates of M will be

= (7 + 1)/2, (-3 + 9)/2 = 8/2, 6/2

= (4, 3)

The slope of line PQ will be = -1/m = -1/ (-2) = ½

Thus, the equation of PQ is

y – 3 = ½ (x – 4)

2y – 6 = x – 4

x – 2y + 2 = 0

(iii) As point (-2, p) lies on the above line

The point will satisfy the line equation

-2 – 2p + 2 = 0

-2p = 0

p = 0

Thus, the value of p is 0.

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