Question

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

Answer 1

`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

`color(purple)(m_(GH) * m_(JG) = -1`

Explanation:

Slope of a line segment is given by formula,

`m = (y2 - y1) / (x2 - x1)`

`m_(GH) = (3 - 2) / (-1-1) = -(1/2)`

`m_(HJ) = (2+1) / (1 + 3) = 3/4`

`m_(JG) = (-1-3) / (-3+1) = 2`

Two line segments are perpendicular to each other,

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

`m_(GH) * m_(JG) = -(1/2) * 2 = -1`

Hence it’s a right triangle