Using Pythagoras with coordinates
We can also use Pythagoras to find the distance between two points.
Example
If A has coordinates (3, 4) and B has coordinates (10, 12), calculate the length of AB.
Answer
Plot the coordinates onto a graph.
Join up A and B to show the line AB then form a right-angled triangle.
\({a^2} = {b^2} + {c^2}\)
\({a^2} = {8^2} + {7^2}\)
\({a^2} = 64 + 49\)
\({a^2} = 113\)
\(a = \sqrt {113}\)
\(a = 10.6\,units\,(to\,1\,decimal\,place)\)
More guides on this topic
- Determine the gradient of a straight line
- Circle geometry
- Calculating the volume of a standard solid
- Applying the properties of shapes to determine an angle
- Using similarity
- Working with two-dimensional vectors
- Working with three-dimensional coordinates
- Using vector components
- Calculating the magnitude of a vector
- An Approximate History of Co-ordinates