# FIND THE MISSING VALUE WITH PERPENDICULAR LINES

Find the Missing Value with Perpendicular Lines :

Here we are going to see how to find the missing value using the concept perpendicular lines.

## Find the Missing Value with Perpendicular Lines - Practice questions

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.

Solution :

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.

Solution :

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)

=  (1-3)/(4-h)

m1  =  -2/(4-h)

Slope of the line 7x – 9y – 19 = 0

m = -7/(-9)  =  7/9

m 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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