Question

If the points ( x, y), (1, 2) and ( -3, 4) are collinear, then

• A. x + 2y - 5 = 0
• B. x + y - 1 = 0
• C. 2x + y - 4 = 0
• D. 2x - y + 10 = 0

Answer 1

Answer: (A)

If (x, y), (1, 2) and (-3, 4) are collinear then slope of line joining (x, 4) and (1, 2) is same as line joining points (1, 2) and ( -3, 4) or line joining (x, 4) to (- 3, 4).
$So,\frac{2-y}{1-x}=\frac{4-2}{-3-1}=\frac{4-y}{-3-x}\Rightarrow \frac{2-y}{1-x}=-\frac{1}{2}$
$\Rightarrow \frac{y-2}{1-x}=\frac{1}{2}\Rightarrow -4+2y=1-x\Rightarrow x+2y-5=0$