Point

In mathematics, a point is a specific location in space. It is represented by a dot and has no size or dimension. A point is usually named using a single capital letter, such as "A".

Properties of a Point

1. Location: A point is a fixed location in space and does not have any length, width, or height.
2. Coordinates: In a coordinate system, a point is represented by an ordered pair of numbers (x, y), where x is the horizontal position and y is the vertical position.
3. Distance: The distance between two points can be calculated using the distance formula: \[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

Example Problems

Let's solve a few example problems to understand points better:

1. Problem 1: Find the distance between the points (3, 4) and (7, 1).

Solution: Using the distance formula: \[ \text{Distance} = \sqrt{(7 - 3)^2 + (1 - 4)^2} = \sqrt{4^2 + (-3)^2} = \sqrt{16 + 9} = \sqrt{25} = 5 \]

2. Problem 2: Plot the point (2, 5) on a coordinate plane.

Solution: Start at the origin (0, 0) and move 2 units to the right on the x-axis and 5 units up on the y-axis to plot the point (2, 5).

Study Guide

Here are some key points to remember about points:

• A point is a specific location in space represented by a dot.
• It has no size or dimensions.
• In a coordinate system, a point is represented by an ordered pair (x, y).
• The distance between two points can be calculated using the distance formula.

Practice plotting points on a coordinate plane and calculating distances between them to strengthen your understanding of points in mathematics.