MCQ
If (a, 0), (0, b) and (x, y) are collinear, then
- Aay - bx = 1
- Bax + by = 1
- Cay + bx = ab
- ✓ax - by = ab
✓
Answer
Correct option: D.
ax - by = ab
(D) ay + bx = ab
Explanation: If given points are collinear, then the area of the triangle formed by these three points is 0.
$\therefore$ Area $=\frac{1}{2}|a(b-y)+0(y-0)+x(0-b)|=0$
$\Rightarrow \frac{1}{2}|a b-a y-b x|=0$
$\Rightarrow a b-a y-b x=0$
$\Rightarrow a y+b x=a b$
Explanation: If given points are collinear, then the area of the triangle formed by these three points is 0.
$\therefore$ Area $=\frac{1}{2}|a(b-y)+0(y-0)+x(0-b)|=0$
$\Rightarrow \frac{1}{2}|a b-a y-b x|=0$
$\Rightarrow a b-a y-b x=0$
$\Rightarrow a y+b x=a b$
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