1
1 The grid shows a point A.
y
4
2
A
1
–4 –3 –2 –1 0 1 2 3 4 x
–1
–2
–3
–4
(a) Write down the coordinates of point A.
( .................... , .................... ) [1]
(b) On the grid, plot the point B at (−1, 3). [1]
(c) C is a point on the grid whose coordinates are whole numbers.
On the grid, mark a point C so that triangle ABC is isosceles. [1]
[Total: 3]
2 The diagram shows a line L and two points, A and B, on a grid.
2
y
6
L
5
A
4
1
B
0 x
–6 –5 –4 –3 –2 –1 1 2 3 4 5 6 7 8
–1
–2
(a) Write down the coordinates of point A.
( .............................. , .............................. ) [1]
(b) (i) Find the gradient of line L.
................................................... [1]
(ii) Write down the equation of line L in the form y = mx + c.
y = ................................................... [2]
(c) (i) Draw a line that is perpendicular to line L and passes through the point A. [1]
(ii) This line crosses the x-axis at point C.
Mark point C on the grid and write down the coordinates of point C.
( .............................. , .............................. ) [1]
[Total: 6]
3 The diagram shows a point P, a shape S and lines A and B on a 1 cm2 grid.
3
y
9
P
8
6
A
S
5
1
B
–2 –1 0 1 2 3 4 5 6 7 8 9 10 x
(a) Line A is parallel to line B.
Explain what parallel means.
.......................................................................................................................................................... [1]
(b) Write down the coordinates of point P.
( .................... , .................... ) [1]
(c) (i) Write down the mathematical name for shape S.
................................................... [1]
(ii) Work out the area of shape S.
................................................... cm2 [1]
(d) (i) Find the gradient of line A.
................................................... [1]
4
(ii) Write down the equation of line A.
................................................... [2]
[Total: 7]
4 A rhombus ABCD has a diagonal AC where A is the point (−3, 10) and C is the point (4, −4).
(a) Calculate the length AC.
................................................... [3]
(b) Show that the equation of the line AC is .
[2]
5
(c) Find the equation of the line BD.
................................................... [4]
[Total: 9]
5 The line crosses the y-axis at G.
Write down the coordinates of G.
( .................... , .................... ) [1]
[Total: 1]
6 The equation of line L is .
(a) Find the gradient of line L.
................................................... [2]
6
(b) Find the coordinates of the point where line L cuts the y-axis.
( .................... , .................... ) [1]
[Total: 3]
7 The coordinates of P are (−3, 8) and the coordinates of Q are (9, −2).
(a) Calculate the length PQ.
................................................... [3]
(b) Find the equation of the line parallel to PQ that passes through the point (6, −1).
................................................... [3]
7
(c) Find the equation of the perpendicular bisector of PQ.
................................................... [4]
[Total: 10]
8 The line L is shown on the grid.
(a) Find the equation of the line L in the form .
y = ................................................... [3]
8
(b) The equation of a different line is .
(i) Write down the gradient of this line.
................................................... [1]
(ii) Write down the co-ordinates of the point where this line crosses the y-axis.
( .............................. , .............................. ) [1]
(c) On the grid, draw the graph of for . [3]
[Total: 8]
9 The points (9, a) and (b, 3) lie on the line .
Work out the value of
(a) a,
a = ................................................... [2]
(b) b.
b = ................................................... [2]
[Total: 4]
10 A is the point (8, 5) and B is the point (−4, 1).
9
(a) Calculate the length of AB.
................................................... [3]
(b) Find the co-ordinates of the midpoint of AB.
( .............................. , .............................. ) [2]
[Total: 5]
11 The diagram shows a straight line L.
(a) Find the equation of line L.
................................................... [3]
10
(b) Find the equation of the line perpendicular to line L that passes through (9, 3).
................................................... [3]
[Total: 6]
12 A is the point (2, 3) and B is the point (7, −5).
Find the equation of the line through A that is perpendicular to AB.
Give your answer in the form y = mx + c.
y = ................................................... [4]
[Total: 4]
11
13
y
6
A
5
4
3
2
1
–8 –7 –6 –5 –4 –3 –2 –1 0 1 2 x
–1
–2
–3
B
–4
–5
–6
–7
–8
A is the point (−6, 5) and B is the point (−2, −3).
(a) Find the equation of the straight line, l, that passes through point A and point B.
Give your answer in the form y = mx + c.
y = ................................................... [2]
(b) Find the equation of the line that is perpendicular to l and passes through the origin.
................................................... [2]
[Total: 4]
12
14 Find the gradient of the line that is perpendicular to the line .
................................................... [2]
[Total: 2]
15 A is the point (5, −5) and B is the point (9, 3).
Find the coordinates of the midpoint of AB.
( ......................., ....................... ) [2]
[Total: 2]
16 A is the point (5, 7) and B is the point (9, −1).
Find the equation of the line AB.
................................................... [3]
[Total: 3]
13
17
y
5
4
l
3
2
1
–3 –2 –1 0 1 2 3 4 5 6 x
–1
–2
–3
(a) Find the gradient of line l.
................................................... [2]
(b) Find the equation of line l in the form y = mx + c.
y = ................................................... [2]
(c) Find the equation of the line that is perpendicular to line l and passes through the point (12, −7).
Give your answer in the form y = mx + c.
y = ................................................... [3]
[Total: 7]
18 The equation of a straight line is .
14
(a) Find the gradient of this line.
................................................... [1]
(b) Find the co-ordinates of the point where the line crosses the y-axis.
( .............................. , .............................. ) [1]
[Total: 2]
19 A is the point (5, 7) and B is the point (9, −1).
Find the length AB.
................................................... [3]
[Total: 3]
20 A is the point (5, −5) and B is the point (9, 3).
Find the length of AB.
........................................ [3]
[Total: 3]
