Coordinates and Midpoints

Understanding Coordinates

A coordinate refers to a position on a graph which is given by an ordered pair of numbers: (x, y).
The first number is the x-coordinate and it shows the position on the horizontal axis.
The second number is the y-coordinate and it shows the position on the vertical axis.
The horizontal axis is also known as the x-axis and the vertical axis is known as the y-axis.
The point where the axes cross is called the origin, and its coordinates are (0,0).

When plotting coordinates, always remember the phrase ‘along the corridor, up the stairs’. This means we first move along the x-axis (horizontally) then up the y-axis (vertically).
Negative numbers in coordinates show a move in the opposite direction. i.e., to the left for the x-axis and downward for the y-axis.
Coordinate positions should not be estimated, precision is essential.

The midpoint is the point exactly in the middle between two other points.
To find the midpoint, use the formula: M = [(x1 + x2)/2 , (y1 + y2)/2]
This formula basically averages the x-coordinates and the y-coordinates of the two points separately.
When using this formula, be careful with negative numbers and fractions.

Mastering coordinates and midpoints requires direct practical handling of problems. Regularly practise plotting points, understanding the positions of coordinates and calculating midpoints.
Use graph paper when practising to ensure you plot points accurately.
Always verify your midpoint calculations on the graph, using this visual check as an additional method to support your learning.