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.