Given that (1, -2), (0, 5) and (-3, 1) are the vertices of a right triangle, how do you determine an equation of the line that passes through the endpoints of the hypotenuse?

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Answer 1 · 2017-10-02T18:42:13

#y=-7x+5.#

Let the gven points be, #A(1,-2), B(0,5), and, C(-3,1).#

The slope #m_1# of line #AB,# is, #(-2-5)/(1-0)=-7.#

The slope #m_2# of line #BC,# is, #(1-5)/(-3-0)=4/3.#

The slope #m_3# of line #CA,# is, #(1-(-2))/(-3-1)=-3/4.#

#because m_2xxm_3=-1, :., BC bot CA.#

#:. /_C# is the right angle.

#:. AB# is the hypotenuse.

Using the Slope-Intercept Form, we get,

#y=-7x+5,# as the desired eqn. of the hypo.