Problem 62 - College Algebra

Question

What is a half-plane?

Step-by-Step Solution

Answer

A half-plane is the area in a coordinate plane that is bound by a line and extends in one direction towards infinity. Each line in a two-dimensional space divides that space into two half-planes.

Step 1: Define Half-Plane

A half-plane is the area in a coordinate plane that is bound by a line (called the boundary line) and extends in one direction towards infinity. It essentially takes the form of a semi-infinite flat surface.

Step 2: Understanding Characteristics

When given a line in a two-dimensional space (the boundary line), there are two half-planes. Each half-plane includes the points that lie on one side of the line. Note that the boundary line could either be part of the half-plane or not, depending on the specific problem or context.

Step 3: Visualization

It might be helpful to visualize this concept. Draw a line on a piece of paper. Everything on one side of the line is one half-plane, and everything on the other side is the other half-plane. The line itself is the boundary.