Question

Find the value of k so that the points A ( -2, 3 ) , B ( 3 , - 1 ) and C ( 5 , k ) be collinear​

Answer 1

Answer:

Three collinear points are,

•A(-2,3) = (x1,y1)

.B(3,-1) = (x2,y2) •C(5,k) = (x3,y3)

We know that given three points are collinear if and on if,

[x1(y2-y3) + x2(y3-y1) + x3(y1-y2)] = 0

=> [-2(-1-k) + 3(k-3) + 5{(3-(-1))}]= O

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

=> (2 + 2k + 3k - 9 + 20) = 0

=> 5k + 13 = 0

=> k = -13/5