An Important Question of class 10 Based on Equation of a Straight Line Chapter of M.L Aggarwal for ICSE BOARD.
Here two co-ordinated are given and prove that it is perpendicular to a given line and does this line bisect the join of given co-ordinated
This is the Question Number 08, Exercise 12.2 of M.L Aggarwal.
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Is the line through (– 2, 3) and (4, 1) perpendicular to the line 3x = y + 1? Does the line 3x = y + 1 bisect the join of (– 2, 3) and (4, 1).
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Slope of the line passing through the points (-2, 3) and (4, 1) is given by
m1 = y2 – y1/ x2 – x1
= (1 – 3)/ (4 + 2)
= -2/6
= -1/3
And, the slope of the line: 3x = y + 1
y = 3x -1
Slope (m2) = 3
Now,
m1 x m2 = -1/3 x 3 = -1
Thus, the lines are perpendicular to each other as the product of their slopes is -1.
Now,
Co-ordinates of the mid-point of the line joining the points (-2, 3) and (4, 1) is
([-2 + 4]/2, [3 + 1]/2) = (1, 2)
Now, if the line 3x = y + 1 passes through the mid-point then it will satisfy the equation
3(1) = (2) + 1
3 = 3
Hence, the line 3x = y + 1 bisects the line joining the points (– 2, 3) and (4, 1).