I want to find some arbitrary point in the plane
$\displaystyle 2x+4y-2z + 10 =0$
Thank you.
Hello, MatteNoob!
The easiest points are the intercepts. .You can "eyeball" the answers!I want to find some arbitrary point in the plane: .$\displaystyle 2x+4y-2z + 10 \:=\:0$
. . $\displaystyle \begin{array}{cccccccc} \text{Let }y = 0,\:z = 0\!: & 2x + 10 &=& 0 & \Rightarrow & x \:=\: \text{-}5 & \Rightarrow & (\text{-}5,0,0) \\ \\[-4mm] \text{Let }x = 0,\:z = 0\!: & 4y + 10&=& 0 & \Rightarrow & y \:=\: \text{-}\frac{5}{2} & \Rightarrow& \left(0,\:\text{-}\frac{5}{2},\:0\right) \\ \\[-4mm] \text{Let }x = 0,\:y=0\!: & \text{-}2z+10 &=& 0 & \Rightarrow & z \:= \:5 & \Rightarrow & (0,\:0,\:5) \end{array}$