Question

If the segment joining the points $(a,b),(c,d)$ subtends a right angle at the origin, then

• A. $ac-bd=0$
• B. $ac+bd=0$
• C. $ab+cd=0$
• D. $ab-cd=0$

Answer 1

The correct option is B $ac+bd=0$

Slope of a line (m)

$m=\frac{y_2-y_1}{x_2-x_1}$

Slope of line AC =$\frac{b}{a}$

Slope of line BC =$\frac{d}{c}$

Line $AC$ and $BC$ are perpendicular,

According to formula,

Slope of line $AC\times$Slope of line $AC=-1$

$\frac{b}{a}$×$\frac{d}{c}=-1$

$bd=-ac$

$ac+bd=0$