Question

The hypotenuse of a right angled triangle has its ends at the points (1, 3) and (-4, 1). Find the equation of the legs (perpendicular sides) of the triangle.

Answer 1

Let ABC be the right angles triangle, where $\angle C={90}^{\circ }$

There are infinity many such lines.

Let m be the slope of $AC$.

$\therefore$ Slope of $BC=\frac{1}{m}$

Equation of $AC:y-3=m(x-1)$

$\Rightarrow x-1=\frac{1}{m}(y-3)$

Equation of $BC:$ $y-1=-\frac{1}{m}(x+4)$

$\Rightarrow x+4=-m(y-1)$

For a given value of m, we can get these equations

For $m=0,y-3=0$; $x+4=0$

For $m\to \infty ,x-1=0$; $y-1=0$