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 _.

The points A 05 B42 and C02 form the vertices of a right triangle in the coordinate plane What is the equation of the line that forms the hypotenuseThe equation class=

Respuesta :

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

[tex](0,5)\text{ and (4,2)}[/tex]

We employ the equation of a line in 2 point form

[tex]\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}[/tex]

Put in the points, we have

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

The equation of the line is,

4y + 3x = 20