Question

10. The line joining the points A(-2 , 3) and B(a , 5) is parallel to the line joining
the points C(0 , 5) and D(-2 , 1). Find the value of a

Answer 1

The line joining the points A(-2 , 3) and B(a , 5) is parallel to the line joining
the points C(0 , 5) and D(-2 , 1).
It means, slope of line AB = slope of line CD

Slope of line AB = (5 - 3)/{a - (-2)} = 2/(a + 2)
slope of line CD = (1 - 5)/(-2 - 0) = -4/-2 = 2
∴ 2/(a + 2) = 2
⇒2 = 2(a + 2)
⇒1 = a + 2
⇒ a = -1

Hence, value of a = -1

Answer 2

Solution :

i ) slope of a line joining the

points A( -2,3) =( x1 , y1 ) and

B( a , 5) = ( x2 , y2 ) is

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

= ( 5 - 3 )/( a + 2 )

m1 = 2/(a + 2 ) ---( 1 )

ii ) Slope of a line joining the

points C(0,5) and D(-2 , 1 ) is

m2 = ( 1 - 5 )/( -2 - 0 )

m2 = (-4)/(-2)

m2 = 2 ----( 2 )

According to the problem given ,

Line AB // line CD

m1 = m2

=> 2/( a + 2 ) = 2

=> 2/2 = a + 2

=> 1 = a + 2

=> 1 - 2 = a

Therefore ,

a = -1

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