Find an equation for the plane consisting of all points that are equidistant from the two points (1, 1, 0) and (0, 1, 1).
A) $x - z = 0$
B) $x - z = 1$
C) $x - y = 0$
D) $x - y = 1$
E) $x + z = 0$
F) $x + z = 1$
G) $x + y = 0$
H) $x + y = 1$

Question

Find an equation for the plane consisting of all points that are equidistant from the two points (1, 1, 0) and (0, 1, 1).
A) $x - z = 0$ 
B) $x - z = 1$ 
C) $x - y = 0$ 
D) $x - y = 1$ 
E) $x + z = 0$ 
F) $x + z = 1$ 
G) $x + y = 0$ 
H) $x + y = 1$

Quizplus · Accepted Answer

The plane equidistant from the points (1, 1, 0) and (0, 1, 1) is perpendicular to the line connecting these points and passes through their midpoint. The vector connecting the points is (-1, 0, 1), and the midpoint is (0.5, 1, 0.5). The equation of the plane can be derived using the normal vector (-1, 0, 1), leading to $x - z = 0$, which is perpendicular to the line segment and bisects it.

Find an Equation for the Plane Consisting of All Points x−z=0x - z = 0x−z=0

Find an Equation for the Plane Consisting of All Points $x - z = 0$