Question

If points (1, 4), (3, -2) and (k, 1) are collinear value of k is
(A) 3 (B) 0
(C) -2 (D) 2

Answer 1

Step-by-step explanation:

let a= ( 1,4 )

let b= ( 3,-2 )

let c = ( k,1 )

Distance between a and b

√ ( x2 - x1 ) ^2 + ( y2 - y1 ) ^2

√ ( 3 - 1 ) ^2 + ( - 2 - 4 ) ^2

√ ( 2 ) ^2 + ( - 6 ) ^2

√ 4 + 36

√ 40

√ 2 × 2 × 10

2√ 10

:. distance between a and b= 2 √10

they are collinear points,then

AB = BC = AC = 2√10

distance between b and c

√ ( x2 - x1 )^2 + ( y2 - y1 ) ^2

2√10 = √ ( k -3 ) ^2 + ( 1 - ( - 2 ) ) ^2

2√10 = √ ( k - 3 ) ^2 + ( 1 + 2 ) ^2

2√10 = √ ( k - 3 )^2 + ( 3 ) ^2

2√10 = √ ( k - 3 ) ^2 + 9

2√10 = 3 ( k -3 )

2√10 = 3k - 9

2√10 + 9 = 3k

2√10 + 9 ÷ 3 = k

2√10 + 3 = k

:. k = 2√10 + 3

I think option is wrong

I hope this is helpful to you