Chapter 6 Coordinate Geometry

(~) square root



1. The distance between point A (x1 , y1) and point B (x2 , y2) , is :

AB = ~((x2 - x1)^2 + (y2 - y1)^2)

2. Midpoint of AB :

AB = ( (x1 + x2)/2 , (y1 + y2)/2 )

3. The point that divides a straight line line AB in the ratio m : n is :

( (nx1 + mx2) /(m + n) , (ny1 + my2) / (m + n) )


a) Area of a triangle

A = 1/2 |x1 x2 x3 x1|
|y1 y2 y3 y1|

= 1/2 | (x1)(y2) + (x2)(y3) + (x3)(y1) - (y1)(x2) - (y2)(x3) - (y3)(x1) |

b) Area of a quadrilateral

= 1/2 |x1 x2 x3 x4 x1|
|y1 y2 y3 y4 y1|

4. Gradient of a straight line

m = (y2 - y1) / (x2 - x1)

m = - (y - intercept) / (x - intercept)

5. Equation of a straight line

a) y = mx + c , m = gradient and c = y - intercept

b) y - y1 = m(x - x1)

c) (y - y1) = (y2 - y1)
(x - x1) (x2 - x1)


d) x/a + y/ b ＝ 1 ， a = x- intercept and b = y - intercept

6. Straight lines which are parallel have the same gradient, that is m1 = m2 and vice versa.

7. Two straight lines are perpendicular to each other if m1 m2 = -1 and vice versa.