Coordinate Geometry & Straight Lines (AQA GCSE Further Maths)

A sketch of the lines  and  is shown.

Work out the area of triangle OPQ.

.................................. units²[3]

M is the midpoint of the line AB.

Work out the values of  and .

 ............................ ............................[2]

Work out the equation of the straight line that is

parallel to the line 
and
intersects the -axis at (4, 0)

[3]

Work out the distance between the points (–3, 7) and (5, 1)

........................ units [2]

Here are four sketch graphs.

Circle the letter of the sketch graph that represents  

[1]

and are points on the line

and (5, 0) are points on the line L.
= 1 : 4

Work out the -coordinate of .

[5]

A straight line passes through the points (−2, 11) and (1, 2)

Work out the equation of the line.
Give your answer in the form

[3]

is a straight line.
is the point (−4, 5)
is the point (20, −7)

Work out the coordinates of .

[4]

Here is a sketch of quadrilateral .

is the midpoint of .

Use gradients to show that is parallel to .

[3]

is the point 
is the point 
is the point 
is the midpoint of .

Work out the values of  and .

[3]

  ..........................  ..........................

In the diagram,

A is the point (15, 0) and B lies on the -axis.

Angle ABC = 90° and tan  = 

Work out the equation of the line BC.

[4]

P  and Q  are points on a straight line with gradient 12

Work out one possible pair of integer values for  and .

..................  ....................[2]

Here is a sketch of triangle ABC.

P is a point on AB.

AP : PB is 3 : 1

Work out the length PC.

Give your answer to 4 significant figures.

 ................................ units[4]

and  are points on a coordinate grid.
Show that the line segments and are perpendicular.

[3]

L is a straight line with equation   

where and are non-zero integers.

At which point does L intersect the -axis?

Circle your answer.

[1]

What is the gradient of a line parallel to L?

Circle your answer.

[1]

Work out the point of intersection of the lines

and 

[4]

and are joined by a straight line.

is a point on .

Work out the coordinates of .

[3]