Question

The point a(0,5) B(4,2) and C(0,2) form the vertices of a right triangle. What is the equation of the line that form the hypotenuse

Answer 1

The required equation of the hypotenuse is 3x + 4y - 20 = 0

Solution:

Given, the points A(0,5), B(4,2), and C(0,2) form the vertices of a right triangle in the coordinate plane.

We are to find the equation of the line that forms the hypotenuse.

Assume the points in the co –ordinate plane, A and C are points on y – axis and B, C are points on a line perpendicular to y – axis. Which means AC and BC are legs of right angle triangle.

Thus, we note that the side AB is the hypotenuse of the triangle ABC.

Slope of a line passing through the points (a, b) and (c, d) is given by:

$m=\frac{d-b}{c-a}$

$\text { So, the slope of } \mathrm{AB} \text { is } \mathrm{m}=\frac{2-5}{4-0}=\frac{-3}{4}$

Since the line AB passes through the point A(0, 5),  so its equation in point slope form will be

$\begin{array}{l}{y-y_{1}=m\left(x-x_{1}\right)} \\\\ {y-5=\frac{-3}{4}(x-0)} \\\\ {4(y-5)=-3 x}\end{array}$

On rearranging terms to get standard form of equation,

3x + 4y -20 = 0

Hence, the required equation of the hypotenuse is found