Question

If (3, 4), (–5, 7) and (x, y) are collinear points, then which of the following is true?

• A. –3x + 8y + 41 = 0
• B. 3x + 8y – 41 = 0
• C. –4x + 3y – 29 = 0
• D. 3x + 4y = 11

Answer 1

The correct option is B 3x + 8y – 41 = 0

Let A(3, 4), B(–5, 7) and C(x, y) be collinear points.

$\therefore Ar\left(\Delta ABC\right)=0$

$\Rightarrow \frac{1}{2}\left|\right[3(7-y)+(-5)(y-4)+x(4-7)\left]\right|=0$

$\Rightarrow 21-3y-5y+20-3x=0$

$\Rightarrow 41-8y-3x=0$

$\Rightarrow 3x+8y-41=0$

Hence, the correct answer is option (b).