Question

find the value of k for which the points (-5,1),(1,k),(4,-2) are collinear​

Answer 1

Answer:

using triangle formula,

1/2(-5(k+2) +1(-3)+4(1-k) = 0

-9k=9

k=-1

Step-by-step explanation:

Answer 2

Answer:

k = -11

Step-by-step explanation:

let

x1=-5 , y1=1

x2= 1  , y2=k

x3=4  , y3=-2

since the points are collinear the area of the triangle must be zero.

therefore, 1/2[x1(y2-y3) + x2(y3-y1) + x3(y1-y2)] = 0

                1/2[5(k-(-2)) +1(-2-1) + 4(1-k)]= 0

                1/2[5(k+2) + 1(-3) +4-4k]=0

                1/2[5k + 10 -3 + 4 -4k]= 0

                1/2[k +11]=0

                k+11 =0

                k =-11

hence, k=-11