Coordinates and ratios

Understanding Coordinates and Ratios

Basic Concepts

• In a coordinate system, coordinates are a set of values that determine the position of a point. For example, in a two-dimensional plane, a point is defined by an ordered pair (x,y).
• A ratio is a comparison between two quantities, showing the relative sizes of two or more values.

Use of Coordinates on Graphs

• Coordinates are often used to plot points on a graph.
• The x-coordinate represents the horizontal position and the y-coordinate represents the vertical position.
• When plotting coordinates on a graph, they are usually written in the format (x,y) and are read from the x-axis first (horizontal), then the y-axis (vertical).

Understanding Ratios

• Ratios can be used to show how much of one thing there is compared to another.
• For example, a ratio of 3:2 indicates there are three of one thing for every two of another.
• Ratios can be simplified by dividing all parts by the same number.

Applying Ratios to Coordinates

• Ratios are not only useful in arithmetic, but they can also be applied to the coordinates of two points on a graph to find points lying in between.
• The point dividing the line between two points (x1,y1) and (x2,y2) in the ratio p:q lies at the coordinates ((px2+qx1)/(p+q), (py2+qy1)/(p+q)).

Importance of Coordinates and Ratios in Graphs

• Understanding and applying coordinates and ratios can be essential when analysing patterns in graphs.
• Correct usage of these principles allows for accurate plotting, as well as the ability to understand and interpret data presented in graphical form.