Question

if the point A[x,2] , B[-3-4] and C[7-5] are collinear,then find the value of ?

Answer 1

The given points are A(x, 2) , B(-3, -4) and C(7, -5).
The points A, B and C are collinear if area of a triangle formed by joining these points is 0.
so, area of Δ ABC = 0
⇒12[x1(y2−y3) + x2(y3−y1) + x3(y1−y2)] =0
⇒12[x(−4+5)−3(−5−2) +7(2+4)] = 0
⇒12[x − 3(−7)+ 7×6] = 0
⇒12[x+21+42] = 0
⇒12[x+63] = 0
⇒x+63 = 0
⇒x = −63