Describe the set of points in space whose coordinates satisfy the given combinat

Question

Describe the set of points in space whose coordinates satisfy the given combination of equations and inequalities. Choose the correct description below for the combination of equations and inequalities given in part (a). A The line through the origin parallel to the y-axis. The half space consisting of the points on and above the xz-plane. The fourth quadrant of the xz-plane. The plane perpendicular to the y-axis at y = 0. Choose the correct description below for the combination of equation, and inequalitics given in part The line through the origin parallel to the x-axis. The half space consisting of the points on and below the yz-plane. the plane perpendicular to the x-axis at x = 0. the fourth quadrant of the yz-plane.

Explanation / Answer

(a) The answer is C, the fourth quadrant of the xz-plane. The condition y=0 tells us that the set we want is a subset of the xz-plane. We want nonnegative x values, and nonpositive z values, so this gives us the 4th quadrant.

(b) The answer is D, the fourth quadrant of the yz-plane. The condition x = 0 tells us that the set we want is a subset of the yz-plane. We want nonnegative y values, and nonpositive z values, so this gives us the 4th quadrant.

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