Question

If the points (t,2t),(-2-6),(3,1) are collinear,then the value of t is

Answer 1

Step-by-step explanation:

let us consider, the points are

A (t , 2t ) = ( x1 , y1 )

B (-2 , -6)= (x2 , y2 )

C ( 3 , 1 )= ( x3 , y3 )

As we have given three points are collinear, therefor if we consider AB and BC as a line then,

Slope of AB = Slope of BC

slope of AB = ( y2 - y1) / (x2 - x1)

= ( -6 - 2t) / (-2 - t)

Now,

slope of BC = (y3 - y2 ) / ( x3 - x2 )

= (1 - ( - 6)) / (3 - (-2))

= ( 7 ) /( 5)

Slope of AB = Slope of BC

( -6 - 2t) / (-2 - t) = ( 7 ) /( 5)

( - 6 - 2t) ( 5 ) = ( 7 ) ( -2 - t)

( -30 - 10t ) = (- 14 - 7t)

- 30 + 14 = -7t + 10t

- 16 = 3t

$\boxed{\textbf{\large{t = - 16 / 3}}}$