The distance between two points
Find the distance between the points (5, 3) and (1, 4).
If you think about this, it's just Pythagoras and what we are finding is the hypotenuse or distance in this case.
The midpoint of a line joining two points
Find the coordinates of the midpoint of the line joining (1, 2) and (3, 1).
The gradient of a line joining two points
Find the gradient of the line joining the points (5, 3) and (1, 4).
The equation of a line using one point and the gradient
Find the equation of the line with gradient 2 passing through (1, 4).
We can work out the equation of a perpendicular line by using the relationship:
Find the equation of the line perpendicular to the line, which passes through the points (1, 3) and (4,9), and goes through the origin.
First, find the equation of the original line: