Points in the plane.

**MatteNoob** · August 14th 2008, 06:34 PM

I want to find some arbitrary point in the plane

$2x+4y-2z + 10 =0$

Thank you.

**ticbol** · August 14th 2008, 06:55 PM

Originally Posted by MatteNoob

I want to find some arbitrary point in the plane

$2x+4y-2z + 10 =0$

Thank you.

Since 3 non-colinear points determine a plane, then try two coordinates and solve or the 3rd coordinate.

2x +4y -2z +10 = 0

Example, try x=1 and y=1,
2(1) +4(1) -2z +10 = 0
-2z = -16
z = 8
Hence, (1,1,8) is a point on the given plane.

**MatteNoob** · August 14th 2008, 10:32 PM

Thank you very much. :]

**Soroban** · August 15th 2008, 09:29 AM

Hello, MatteNoob!

I want to find some arbitrary point in the plane: . $2x+4y-2z + 10 \:=\:0$

The easiest points are the intercepts. .You can "eyeball" the answers!

. . $\begin{array}{cccccccc} \text{Let }y = 0,\:z = 0\!: & 2x + 10 &=& 0 & \Rightarrow & x \:=\: \text{-}5 & \Rightarrow & (\text{-}5,0,0) \\ \\[-4mm] \text{Let }x = 0,\:z = 0\!: & 4y + 10&=& 0 & \Rightarrow & y \:=\: \text{-}\frac{5}{2} & \Rightarrow& \left(0,\:\text{-}\frac{5}{2},\:0\right) \\ \\[-4mm] \text{Let }x = 0,\:y=0\!: & \text{-}2z+10 &=& 0 & \Rightarrow & z \:= \:5 & \Rightarrow & (0,\:0,\:5) \end{array}$

**TKHunny** · August 15th 2008, 01:32 PM

or...

$\frac{x}{-5}\;+\;\frac{y}{-5/2}\;+\;\frac{z}{5}\;=\;1$

They're just kind of staring at you in this form.

**MatteNoob** · August 16th 2008, 12:24 PM

Thanks to all of you. I now understand how finding (or checking if) points (are in) the plane. :]

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