Use Ratio to Find the Coordinates of a Point on a Line Given the Coordinates of 2 Other Points

Revision Content: Finding a Point Using Ratio

When calculating coordinates, you might need to find a point that divides a line into a certain ratio. This is possible if you have the coordinates of two other points on the line.

Understanding Ratio

A ratio shows the relative sizes of parts of a whole.
The ratio A:B indicates there are A parts and B parts.
A ratio of 2:3 between points A(x1, y1) and B(x2, y2) means the line is divided into 2 parts from A to the unknown point, and 3 parts from the unknown point to B.

Finding a Point using Ratio

The formula for finding a point that divides a line segment into a given ratio is:
- Let the point be (x, y), and let the ratio be m:n.
- x = (mx2 + nx1)/(m+n)
- y = (my2 + ny1)/(m+n)

Practical Application

For example, if you have to find a point that divides the line joining the points A(-1,3) and B(9,5) in the ratio 2:3,

Substituting the known values into the formula:
- x = (29 + 3(-1))/(2+3)
- y = (25 + 33)/(2+3)

Calculate the value of x and y to get the coordinates of the point.

Remember to practise a wide range of questions on this topic to ensure you understand the concept well.