COORDINATE GEOMETRY Summary

Distance between two points. In general, x1x1 x2x2 y1y1 y2y2 A(x 1,y 1 ) B(x 2,y 2 ) Length = x 2 – x 1 Length = y 2 – y 1 AB 2 = (y 2 -y 1 ) 2 + (x 2 -x 1 ) 2 Hence, the formula for Length of AB or Distance between A and B is y x

The mid-point of two points. x1x1 x2x2 y1y1 A(5,3) B(18,17) Look at it’s horizontal length Look at it’s vertical length Mid-point of AB y x y2y2 Formula for mid-point is

Gradient In general, x1x1 x2x2 y1y1 y2y2 A(x 1,y 1 ) B(x 2,y 2 ) Length = x 2 – x 1 Length = y 2 – y 1 y x θ

Equation of Straight Line Equation of a straight line (gradient-intercept form): y = mx + c where m is the gradient and c is the y-intercept. Equation of a straight line (given gradient and 1 point):

Collinear Points 3 points are collinear if gradient AB = gradient BC A B C

Perpendicular Lines Two lines with gradients m 1 and m 2 are perpendicular if

Perpendicular Bisector Bisector means to cut (bisect) the line into 2 equal parts

Perpendicular Bisector

Area Area of a Polygon. Three points, and. The area of triangle ABC is given by This formula may be extended to a n sided polygon with n vertices. The area is then given by

Equation of Circles

General Form where r is the radius and (a, b) is the centre.

Centre (0, 0), radius 1

Centre (4, −3) and circle touches x-axis Radius = 3

Example Given equation of circle is, find its centre and radius. Centre is (3, 2) and radius is 2