Find the value of 'k', for which the points (8, 1), (k, -4), (2, -5) are collinear.
3
The three points will be collinear if the Δ formed by these points has an area equal to zero.
Let A(8, 1), B(k, -4) and C(2, -5) be the vertices of a triangle.
∴ The given points will be collinear, if ar (ΔABC)=0
∵ Area of triangle having coordinates (x1,y1), (x2,y2), (x3,y3) is 12×|(x1)(y2−y3) + (x2)(y3−y1) + (x3)(y1−y2)|
∴12[8(−4+5)+k(−5−1)+2(1+4)]=0⇒8−6k+10=0⇒6k=18⇒k=3