Question

The points A (0,5), B(4,2), and C(0,2) form the vertices of a right triangle in the coordinate plane. What is the equation of the line that forms the hypotenuse?The equation of the line is _.

Answer 1

The equation of the line that forms the hypotenuse can be gotten, we can utilize two points on that line

`(0,5)\text{ and (4,2)}`

We employ the equation of a line in 2 point form

`(y-y_1)/(x-x_1)=(y_2-y_1)/(x_2-x_1)`

Put in the points, we have

`\begin{gathered} (y-5)/(x-0)=(2-5)/(4-0) \\ (y-5)/(x)=(-3)/(4) \\ 4(y-5)=-3x \\ 4y-20=-3x \\ 4y+3x=20 \end{gathered}`

The equation of the line is,

4y + 3x = 20