You start by finding the slope : y2 - y1 / x2 - x1
2 - 8 / 4 - (-16)
- 6 / 20
m = - 3 / 10
Point slope form : y - y1 = m( x- x1 )
You can pick either of the coordinates and substitute them in
POINT SLOPE FORM EQUATION : y - 8 = -3/10 ( x + 16 )
4x -3y + z = -10...............(1)
2x +y + 3z = 0...............(2)
-x +2y - 5z = 17...............(3)
First we multiply 3*(2) and add it to (1)
6x +3y +9z =0..................+(1)..................> 10x + 10z = -10......(4)
Then we multiply -2*(2) and add it to (3)
-4x -2y -6z =0 ...................+(3)................> -5x -11z = 17...........(5)
Multiply 2*(5) and add it to (4)
-10x -22z = 34...................+(4).................> -12 z = 24 ..............>>> z = -2
Substitute z in (4)............> 10x +10(-2) = -10.............................>>> x = 1
Substitute x and z in (2).....> 2(1) +y + 3(-2) = 0..................>>> y = 4
Solution (x,y,z) = (1,4,-2)
A quadrilateral is a polygon. [always]
