2.12 Coordinate Geometry

P is the point (16, 9) and Q is the point (22, 24).

N is the point on PQ such that PN = 2NQ.
Find the co-ordinates of N.

(.................... , ....................)

and are two points.

Point  has coordinates (—2, 4).
Point  has coordinates (8, 9).

is the midpoint of the line segment .

Find the coordinates of .

 is the point with coordinates (100, 56).

Does point lie on the straight line that passes through  and ?
You must show how you work out your answer.

The points  and  lie in order on a straight line.

The coordinates of  are (2, 5)
The coordinates of  are (4, )
The coordinates of  are (, 17)

Given that , find the values of  and .

A triangle has vertices  and .

The coordinates of  are (—3, —6)
The coordinates of  are (1, 4)
The coordinates of  are (5, —2)

 is the midpoint of .
 is the midpoint of .

Prove that  is parallel to .
You must show each stage of your working.

and  are straight lines.
Line has equation 
Line goes through the points  and 

Do lines and intersect?
You must show all your working.

A rhombus has a diagonal where is the point  and C is the point 

Calculate the length

is the point and is the point .

Calculate the length of  

Find the co-ordinates of the midpoint of  
 

( ..................... , ..................... )

is the point and is the point .

Find the length of .

Find the mid-point of  where and  .
Give your answer in its simplest form in terms of ,  and .
 

..................... , .....................

Calculate the length of AB.

C is the point (8, 14).

Calculate the length of AC.

Find the co-ordinates of the mid-point of BC.
 

( ..................... , ......................)