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

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:

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

On rearranging terms to get standard form of equation,

3x + 4y -20 = 0

Hence, the required equation of the hypotenuse is found

for this case we have by definition, if two lines are perpendicular, then the product of their slopes is -1.

then, given the following line:

so,

we are looking for m_ {2}:

then, the line is given by:

we find "b" replacing the given point:

finally, the equation is:

option c