Question

If the points (1, 3) , (0, 4) and (k, -2) are collinear, then k =

Answer 1

Answer:

Given that,

A(1,3), B(0,4), C(k,-2)

if the points are collinear, then area of the triangle is equal to zero.

area of ∆ABC=1/2|x1(y2-y3)+x2(y3-y1)+x3(y1-y2)|

0=1/2|1(0+2)+0(-2-3)+k(3-4)|

0×2=|1(2)+0+k(-1)|

0=|2-k|

0=2-k

k=2

therefore, the required value of k=2.