Formulas

The Gradient of a Line Joining Two Points


Apply the following formula when finding the gradient of the line joining the points (x1, y1) and (x2, y2):

y2 - y1/ x2 - x1

Example:

Find the gradient of the line joining the points (3, 2) and (4, 6).

Gradient = 6 - 2/4 - 3= 4/1 = 4

The Midpoint of a Line Joining Two Points

When finding the midpoint of the line joining the points (x1, y1) and (x2, y2) apply the following formula:

 [½(x1 + x2), ½(y1 + y2)]

Example

Find the coordinates of the midpoint of the line joining (3, 2) and (5, 3).

Midpoint = [½(5 + 3), ½(2 + 3)] = (4, 2.5)

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Parallel and Perpendicular Lines

When two lines are parallel, they have the same gradient.
When two lines are perpendicular, the product of the gradients of the two lines are -1.

Example:

a) y = 2x + 1
b) y = -½ x + 2
c) ½y = x - 3

The gradients of the lines are 2, -½ and 2 respectively. Therefore (a) and (b) and perpendicular, (b) and (c) are perpendicular and (a) and (c) are parallel.

The Equation of a Line Using One Point and the Gradient

The equation of a line which has gradient m and which passes through the point (x1, y1) is:

y - y1 = m(x - x1)

The equation of a line passing through (x1, y1) and (x2, y2) can be written as:

y - y1 = y2 - y1

x - x1 x2 - x1

References:
http://www.onlinemathlearning.com/coordinate-geometry.html
http://www.mathsrevision.net/alevel/pages.php?page=6