Question

if points (x, -1),(2,1) and (4,5) are collinear find the value of x

Answer 1

If three points are collinear then area of triangle will be 0

[1/2(x1(y2-y3) +X2(y3-y1)+X3(y1-y2)] = 0

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

[1/2(x(-4)+2(6)+4(-2)] = 0

[1/2 (-4x+12-8)] = 0

-4x+4 = 0

-4x = -4

x = -4/-4 = 1

thus the value of x is 1