Find an equation describing all points that are equidistant from the points A(-3, 0, 4) and B(2, 1, 5). What does this equation describe geometrically?
A) 10x + 2y + 2z = 5, the plane that right bisects the line segment AB
B) 10x - 2y + 2z = 5, the plane that right bisects the line segment AB
C) 10x - 2y + 18z = 5, the plane that right bisects the line segment AB
D) 10x + 2y + 18z = 5, the plane that right bisects the line segment AB
E) 10x + 2y + 2z = 5, the plane that contains the points A and B

Question

Quizplus · Accepted Answer

The equation of the plane that is equidistant from points A and B is derived by finding the perpendicular bisector of the line segment AB. The midpoint of AB is (-0.5, 0.5, 4.5), and the normal vector is the difference of the coordinates of B and A, which is (5, 1, 1). The equation of the plane is 10x + 2y + 2z = 5.

Find an Equation Describing All Points That Are Equidistant from the Points