Question

if three points (1,3) , (-2,1) , (k,1) are collinear, then find the value of k
a) 0
b) 5
c)-5
​

Answer 1

Let A (1,3)=(x1, y1)

Let B (-2,1)=(x2, y2)

Let C (K, 1)= (x3, y3)

Points A, B, C are collinear.

Area of triangle ABC =0

Area of triangle ABC=1/2*(x1(y2-y3)+ x2(y3 -y1) +x3(y1 -y2)

=>0=1/2*(1(1-1)+(-2)(1-3)+k(3-1)

=>0=1*0+(-2)*(-2) +k(2)

=>0=0+4+2k

=>0=4+2k

=>-4=2k

=>-2=k

hope it helps..