Find the Missing Value with Perpendicular Lines :
Here we are going to see how to find the missing value using the concept perpendicular lines.
Question 6 :
Find the values of p for which the straight lines 8px + (2-3p)y + 1 = 0 and px + 8y + 7 = 0 are perpendicular to each other.
If two lines are perpendicular then product of their slopes will be equal to -1.
Slope (m) = - coefficient of x/coefficient of y
Slope of the first line 8px + (2-3p)y + 1 = 0
m1 = -8p/(2-3p)
Slope of the second line px + 8y + 7 = 0
m2 = -p/8
m1 ⋅ m2 = -1
[-8p/(2-3p)] ⋅ [-p/8] = -1
[(8 p²)/8(2-3p)] = -1
p²/(2-3p) = -1
p² = -1(2-3p)
p² = -2 + 3 p
p²- 3 p + 2 = 0
(p - 2) (p - 1) = 0
p - 2 = 0 (or) p - 1 = 0
p = 2 (or) p = 1
Question 7 :
If the straight lines passing through the points (h,3) and (4,1) intersects the line 7x – 9y – 19 = 0 at right angle,then find the value of h.
The required straight lines passing through the points (h,3) and (4,1) intersects the line 7x – 9y – 19 = 0 at right angle
Since the line joining the points (h, 3) and (4, 1) and the line 7x - 9y - 19 = 0 are perpendicular the product of their slopes will be equal to -1
m = (y2-y1)/(x2-x1)
m1 = -2/(4-h)
Slope of the line 7x – 9y – 19 = 0
m = -7/(-9) = 7/9
m1 ⋅ m2 = -1
[-2/(4-h)] x (7/9) = -1
[2/(4-h)] x (7/9) = 1
14/9(4-h) = 1
14/(36-9h) = 1
14 = 36 - 9 h
9h = 36-14
9h = 22
h = 22/9
After having gone through the stuff given above, we hope that the students would have understood, Find the Missing Value with Perpendicular Lines.
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