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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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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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.