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

da freeck kinda math is this just drop out

step-by-step explanation:

one way is to plot 2 points and connect them which is what the answer choices seem to be doing

it seems to be using the y intercept and the slope

y=mx+b, m=slope, b=y-intercept (where the line hits the y axis)

slope=rise/run

y-intercept is where the line croses the y axis which is the y value where x=0

you seem to have given the wrong slope (you didn't put a number in front of te x, it should be 2/3 or 3/2 looking at the answer options)

y=? x-1

m=? because of your fault

b=-1

so it has a slope of ? and y intercept of -1, meaning it pases through (0,-1)

so draw point (0,-1) (so answer is one of the first 2 option)

if slope is 2/3, then go up 2 and right 3 then draw line through those 2 points

if slope is 3/2, then go up 3 and right 2 then draw line through those 2 points