Problem 89 - Algebra and Trigonometry

Question

What is a half-plane?

Step-by-Step Solution

Answer

A half-plane is one of the two regions into which a plane is divided by a line, called a boundary. There are two types of half-planes: open half-plane, where points on the boundary are not included, and closed half-plane, where points on the boundary are included.

Step 1: Define a Half-Plane

A half-plane is the region of the plane on one side of a line. We could mention that the line, which partitions the plane into two half-planes, is called a boundary line or just boundary.

Step 2: Classify Half-Planes

Half-planes can be classified into two types: open half-plane and closed half-plane. The difference lies on whether the boundary line is included or not in the half-plane. In an open half-plane, points on the line that makes up the boundary are not considered part of the half-plane. In a closed half-plane, the points on the line that makes up the boundary are considered part of the half-plane.

Step 3: Illustrating Examples

It can be helpful to visualize these concepts with a sketch. Imagine drawing a continuous line on a piece of graph paper. The region on one side of that line represents one half-plane, and the region on the other side represents another half-plane.