Question

11. The line joining the points A(0, 5) and B(4, 2) is perpendicular to the line joining
the points C(-1, -2) and D(5, b). Find the value of b.

Answer 1

The line joining the points A(0, 5) and B(4, 2) is perpendicular to the line joining
the points C(-1, -2) and D(5, b).
It means, slope of line AB × slope of line CD = -1 [ because we know, if two lines of slope m₁ and m₂ are perpendicular to each other then, product of slope of line = -1 ]

slope of line AB = (2 - 5)/(4 - 0) = -3/4
slope of line CD = {b - (-2)}/{5 -(-1)} = (b + 2)/(5 + 1) = (b + 2)/6
∴ -3/4 × (b + 2)/6 = -1
⇒(b + 2) = 8
⇒ b = 8 - 2 = 6

Hence, value of b = 6

Answer 2

Solution :

i ) Slope of line joining

A( 0,5) = ( x1 , y1 ) and

B(4,2) = ( x2 , y2 )

m1 = ( y2 - y1 )/( x2 - x1 )

= ( 2 - 5 )/( 4 - 0 )

= -3/4 ---( 1 )

ii ) Slope of a line joining

C( -1 , -2 ) and D( 5 , b )

m2 = ( b +2 )/( 5 + 1 )

m2 = ( b +2 )/6 ----( 2 )

iii ) According to the problem

given ,

AC is perpendicular to CD.

m1 × m2 = -1

=> ( -3/4 ) × ( b +2 )/6 = -1

=> b+2 = [( -1 ) × 6 × 4 ]/( -3 )

=> b +2 = 8

=> b = 8 -2

b = 6

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