# Thread: Coordinated Geometry

1. ## Coordinated Geometry

Given that A is the point (0,11), B is the point (8,5) and O is the origin , calculate
How to find the,
a) the coordinates of M , the mid point of AB,
b) the gradient of OM,
c) the lenght of the line AB,
d) the equation of the line AB

2. Originally Posted by Sohail
Given that A is the point (0,11), B is the point (8,5) and O is the origin , calculate
How to find the,
a) the coordinates of M , the mid point of AB,
From the average of the x coordinate and y coordinates.
(8+0)/2=4 and (11+5)/2=8. Thus, the point is (4,8).
b) the gradient of OM,
Same as the slope of AB because it is part of the same line.
Thus, (11-5)/(0-8)=(-6)/(-8)=3/4
c) the lenght of the line AB,
Use the distance formula,
(0-8)^2+(11-5)^2=8^2+6^2=64+36=100
But that is the square of the distance. Take the square root,
10
d) the equation of the line AB
The y-intercept is 11 because you have (0,11) and x=0 at that point.
Thus, the equation is,
y=(3/4)x+11