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Chapter 7: Problem 53

What is a half-plane?

Short Answer

Expert verified
A half-plane is one of the two regions into which a plane is divided by a line.

Step by step solution

01

Definition of a Plane

A Plane is a flat, two-dimensional surface that extends infinitely far. In coordinate geometry, a plane is something we often deal with.
02

Dividing a Plane

A plane can be divided into two equal and infinite parts by a line on the plane. This line is known as the dividing line.
03

Half-Plane Definition

Each of the two infinite parts created by the dividing line is known as a half-plane. Therefore, a half-plane can be defined as one of the two regions of the plane that is divided by a line.

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Most popular questions from this chapter

In Exercises 9-14, a. Determine if the parabola whose equation is given opens upward or downward. b. Find the vertex. c. Find the \(x\)-intercepts. d. Find the \(y\)-intercept. e. Use (a)-(d) to graph the quadratic function. \(y=x^{2}+8 x+7\)

Make Sense? Determine whether each statement makes sense or does not make sense, and explain your reasoning. When graphing \(3 x-4 y<12\), it's not necessary for me to graph the linear equation \(3 x-4 y=12\) because the inequality contains a \(<\) symbol, in which equality is not included.

Graph each linear inequality. \(3 x+y \leq 3\)

Write each sentence as an inequality in two variables. Then graph the inequality. The \(y\)-variable is at least 2 more than the product of \(-3\) and the \(x\)-variable.

Graph the solution set of each system of inequalities. \(\left\\{\begin{array}{r}x+y<4 \\ 4 x-2 y<6\end{array}\right.\)
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