Coordinate Geometry

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 .

and  are points on a grid.

is the point with coordinates (106, 103)
is the point with coordinates (106, 105)
is the point with coordinates (104, 105.5)

and are two other points on the grid such that

    is the midpoint of
    is the midpoint of

Work out the coordinates of the point .

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.

A pattern is made from four identical squares.

The sides of the squares are parallel to the axes.

Point  has coordinates (6, 7)
Point  has coordinates (38, 36)
Point  is marked on the diagram.

Work out the coordinates of .

 is a line segment.

 is the point with coordinates (3, 6, 7).
The midpoint of  has coordinates (—2, 2, 5).

Find the coordinates of .

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

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

The diagram shows a line joining  to .

The gradient of the line is 2

The length of the line is 

Work out the coordinates of 

A rectangle is to be drawn on a centimetre grid such that

has coordinates (–4, –2)
has coordinates (1, 10)
has coordinates (19, )
has coordinates

Work out the value of , the value of and the value of .

Calculate the perimeter, in centimetres, of rectangle ABCD.

...................................................... cm

A pattern is made from four congruent right-angled triangles.

The line AC is parallel to the x - axis.
The point A has coordinates (4, 9) and the point B has coordinates (17, 12).

Work out the coordinates of point C and point D.

A straight line goes through the points () and (), where

Find the gradient of the line.

Point has coordinates (5, 7).
Point has coordinates (1, 2.5).

Point is the midpoint of the line .

Find the coordinates of point .

is the point (2, 14)
is the point (6, 8)
is the point (2, 5)

Use gradients to show that angle is not a right angle.

(0, 2) and  (6, 5) are points on the straight line .

Work out the coordinates of .

 is the point (2, –5)

is the point (4, –9)

Show that the gradient of the straight line passing through and is –2.

is the point (–301, 601)

Does lie on the straight line passing through and ?

You must show your working.

and  are points on the axes as shown.

The area of triangle  is 28 square units.

Work out possible coordinates for  and .

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

 ( ......... , .......... )

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

Point has coordinates
Point  has coordinates
The midpoint of  has coordinates 

Find the value of  and the value of .

a = ................................................     
b = ................................................     

The straight line has equation     
The curve has equation

and intersect at the points and .

Find the coordinates of the midpoint of .
Show clear algebraic working.

Triangle  is isosceles with  and 

is the point with coordinates 
is the point with coordinates  where
is the point with coordinates 

is the midpoint of .
The gradient of  is 2

Find the value of and the value of .

The curve with equation and the straight line with equation  intersect at the points and .

Work out the exact length of 
Show your working clearly and give your answer in the form  where  is an integer.

The curve with equation  and the line with equation  intersect at the points  and .

Find the coordinates of the midpoint of .
Show your working clearly.