Describe the given set of points with a single equation or with a pair of equations.
-The plane through the point (-7, -3, 2) and parallel to the xy-plane
A) x + y + 2 = 0
B) x + y = -10
C) z = 2
D) x = -7 and y = -3

Question

Quizplus · Accepted Answer

A plane parallel to the xy-plane will have the equation z=k where k is a constant since it does not depend on z. Since the point (-7,-3,2) is on the plane, we can see that the equation of the plane is z=2. Choice A is not a valid equation for a plane in 3 dimensions. Choice B is the equation of a line in the xy-plane. Choice D gives two separate equations for x and y, but does not give an equation for the entire plane.

Describe the Given Set of Points with a Single Equation