Coordinate Geometry

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.

is a triangle in which angle

and are integers such that

the coordinates of are
the coordinates of are (–1, –5 )
the coordinates of are

Given that the gradient of is 
work out the value of and the value of

p = .......................................................
q = .......................................................

Here is a cuboid drawn on a 3-D grid.

 is a vertex of the cuboid.

divides the line  in the ratio 1 : 2

Find the coordinates of .

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 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 .

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.

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

Point is the midpoint of the line .

Find the coordinates of point .