1.
Two sides of a square are shown on the grid.
y
4
A
3
B
2
1
O
1
3
2
4
5
6
7
8
x
–1
–2
–3
(a)
C
Write down the coordinates of A.
Answer ( ……………………. , ……………………. )
(1)
(b)
Write down the coordinates of C.
Answer ( ……………………. , ……………………. )
(1)
(c)
Draw two more lines to complete the square ABCD.
(1)
(d)
M is the mid-point of AC.
Work out the coordinates of M.
Answer ( ……………………. , ……………………. )
(2)
(Total 5 marks)
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1
2.
The points P, Q and R are plotted on the grid to form a triangle.
y
6
Q
5
4
3
R
2
1
P
0
0
(a)
1
2
3
4
5
6
7
9 x
8
What is the mathematical name given to triangle PQR?
Answer .........................................................................
(1)
(b)
(i)
Mark the mid-point of PQ on the grid.
Label it M.
(1)
(ii)
Write down the coordinates of M.
Answer (............................, ...............................)
(1)
(Total 3 marks)
3.
The diagram shows the positions of A (2, 5) and B (4, 1).
y
6
A
4
2
B
x
–4
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–2
0
2
4
2
Find the coordinates of M, the mid-point of the line AB.
...............................................................................................................................................
...............................................................................................................................................
...............................................................................................................................................
Answer...................................................................................................................................
(Total 2 marks)
4.
A line AB is shown on the grid.
y
7
6
5
A
4
P
3
2
1
B
0
0
(a)
1
2
3
4
5
6
7
8
9
x
Mark the mid-point of AB.
Label it M.
(1)
(b)
Write down the coordinates of M.
Answer ( ................. , .................)
(1)
(c)
Draw a line through the point P, parallel to the line AB.
(1)
(Total 3 marks)
The Robert Smyth School
3
5.
The triangle ABC is shown on a centimetre grid.
y
5
B
4
3
2
1
0
(a)
A
0
1
2
C
3
4
5
6 x
Find the coordinates of the midpoint of BC.
.....................................................................................................................................
Answer ( ..............................., ..............................)
(2)
(b)
Find the area of the triangle ABC.
.....................................................................................................................................
.....................................................................................................................................
Answer ..................................................................cm2
(2)
(c)
Show, on the grid below, how two triangles congruent to triangle ABC can be put together
to form an isosceles triangle.
(2)
(Total 6 marks)
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4
1.
(a)
(2, 3)
B1
If both reversed ie (3, 2) and (–3, 6)
SC1
(b)
(6, –3)
B1
(c)
2 correct lines ± 2 mm meeting at (1, –2)
Condone broken lines
B1
(d)
Look for answer (4, 0)
If (4, 0) not seen, award M1 for position (4, 0) ± 2 mm
clearly marked
If both reversed in (a) and (b) and (0,4) in (d)
SC1
M1 A1
[5]
2.
(a)
Isosceles
B1
(b)
(i)
Point marked on diagram
Condone missing label if point is clear
B1
(ii)
(2,3)
B1 ft
[3]
3.
(– 2 + 4) / 2 oe
M1
or (5+1) / 2
(1,3)
A1
[2]
4.
(a)
Mid-point indicated at (4,2)
 2mm; letter M not necessary
(b)
(4, 2)
(c)
Correct line through P
At least 3cm long; check whether the line, if produced, would go
within 2mm of (5, 4) and (9,2)
B1
B1ft
B1
[3]
5.
05 –42
or
2
2
M1
or evidence of good use of grid
2.5, –1
A1
Take one or other value correct as
evidence for the M1
SC1 for (–1, 2.5)
[2]
6.
(a)
(4, 2.5) or (x4, y2.5)
B1 for each B1 if wrong way
B2
(b)
½×2×3
M1
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(c)
3 cm2
A1
Correct 2 triangles to 2mm accuracy
B1 if triangles correct orientation but
not touching along common side
B1 any 2 congruent triangles
B1 any isosceles triangle
B2
[6]
The Robert Smyth School
6