The coordinates of the vertices of △GHJ are G(−1, 3) , H(1, 2) , and J(−3, −1) HELP ME PLEASE! fill them in? down below

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Answer 1 · 2018-02-16T08:24:31

$m_{H J} = \frac{3}{4}, m_{J G} = 2$ $m_(HJ) = color(red)(3/4), m_(JG) =color(blue)( 2$ .

Delta GHJ is a right triangle because two of these slopes have a product of -1

$m_{G H} \cdot m_{J G} = - 1$ $color(purple)(m_(GH) * m_(JG) = -1$

Slope of a line segment is given by formula,

$m = \frac{y 2 - y 1}{x 2 - x 1}$ $m = (y2 - y1) / (x2 - x1)$

$m_{G H} = \frac{3 - 2}{- 1 - 1} = - (\frac{1}{2})$ $m_(GH) = (3 - 2) / (-1-1) = -(1/2)$

$m_{H J} = \frac{2 + 1}{1 + 3} = \frac{3}{4}$ $m_(HJ) = (2+1) / (1 + 3) = 3/4$

$m_{J G} = \frac{- 1 - 3}{- 3 + 1} = 2$ $m_(JG) = (-1-3) / (-3+1) = 2$

**Two line segments are perpendicular to each other, **

if the product of their slope is equal to $- 1$ $color(red)(-1$

$m_{G H} \cdot m_{J G} = - (\frac{1}{2}) \cdot 2 = - 1$ $m_(GH) * m_(JG) = -(1/2) * 2 = -1$

Hence it’s a **right triangle **