Correct Answer - Option 1 : 5x + y - 11 = 0
Formula used:
Area of triangle:
Let coordinates be A(x1, y1), B(x2, y2) and C(x3, y3),
then the area of a triangle is given as,
Δ = \(\frac{1}{2}\)[x1 ( y2 - y3 ) + x2 ( y3 - y1 ) + x3 ( y1 - y2 )]
Calculation:
Given that,
A(1, 6), B(3, -4) and C(x, y) are collinear.
⇒ Area of Δ ABC = 0
∵ Δ = \(\frac{1}{2}\)[x1 ( y2 - y3 ) + x2 ( y3 - y1 ) + x3 ( y1 - y2 )]
⇒ \(\frac{1}{2}\)[1(-4 - y) + 3(y - 6) + x[6 - (-4)] = 0
⇒ -4 - y + 3y - 18 + 6x + 4x = 0
⇒ 10x + 2y - 22 = 0
⇒ 5x + y - 11 = 0
