Question 1008730: Find an equation of the plane that passes through the points
(-1, 0, -4),(2, 1, 8),and(-1, 1, -1).(Suggestion: The equation of a plane can be written as z = ax + by + c.)
z=
Answer by Edwin McCravy(20054)   (Show Source):
You can put this solution on YOUR website!
z = ax + by + c
Substitute (x, y, z) = (-1, 0, -4)
-4 = a(-1) + b(0) + c
-4 = -a + c
a - c = 4
Substitute (x, y, z) = (2, 1, 8)
8 = a(2) + b(1) + c
8 = 2a + b + c
-2a - b - c = -8
2a + b + c = 8
Substitute (x, y, z) = (-1, 1, -1)
-1 = a(-1) + b(1) + c
-1 = -a + b + c
a - b - c = 1
So we have this system of equations:
That's easy to solve for a, b, and c.
The substitute the vales you get for a,b, and c
in z = ax + by + c to get your answer.
Want to see your plane graphed in 3D? Look below.
It's the plane in which the green triangle is in.
Edwin
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