The diagram shows a coordinate grid. The x-axis and y-axis are both numbered from 0 to 8. Four points are plotted: A is 2 units across and 5 units up from the origin. B is 6 units across and 1 unit up. C is on the y-axis, 4 units up from the origin. D is on the x-axis, 7 units across from the origin.
(a)Write down the coordinates of point A.(1)
(b)Write down the coordinates of point B.(1)
(c)Write down the coordinates of point C.(1)
(d)Write down the coordinates of point D.(1)
(Total for Question 1 is 4 marks)
2
A coordinate grid has the x-axis and y-axis both numbered from 0 to 10. Plot each of the following points on the grid and label it with the correct letter.
(a)Plot the point E(3, 7).(1)
(b)Plot the point F(9, 2).(1)
(c)Plot the point G(0, 6).(1)
(d)Plot the point H(5, 0).(1)
(Total for Question 2 is 4 marks)
3
Answer the following questions about a coordinate grid.
(a)Write down the coordinates of the origin.(1)
(b)A point lies on the y-axis, 5 units above the origin. Write down the coordinates of this point.(1)
(Total for Question 3 is 2 marks)
4
The diagram shows a coordinate grid. The x-axis and y-axis are both numbered from -6 to 6. Point P is plotted 3 squares to the left of the y-axis and 4 squares above the x-axis. Point Q is plotted 5 squares to the right of the y-axis and 2 squares below the x-axis. Point R is plotted 4 squares to the left of the y-axis and 5 squares below the x-axis. Point S is plotted 3 squares to the right of the y-axis and 6 squares above the x-axis.
(a)Write down the coordinates of point P.(1)
(b)Write down the coordinates of point Q.(1)
(c)Write down the coordinates of point R.(1)
(d)Write down the coordinates of point S.(1)
(Total for Question 4 is 4 marks)
5
A coordinate grid has the x-axis and y-axis both numbered from -6 to 6. Plot each of the following points on the grid and label it with the correct letter.
(a)Plot the point T(-5, -3).(1)
(b)Plot the point U(4, 5).(1)
(c)Plot the point V(-2, 6).(1)
(d)Plot the point W(6, -4).(1)
(Total for Question 5 is 4 marks)
6
For each point below, state whether it lies in the top-right, top-left, bottom-left or bottom-right region of a coordinate grid.
(a)(-4, 2)(1)
(b)(5, -6)(1)
(c)(-7, -1)(1)
(Total for Question 6 is 3 marks)
7
The point (-3, 8) is plotted on a coordinate grid. Decide whether each statement is True or False.
(a)The point lies to the left of the y-axis.(1)
(b)The point lies below the x-axis.(1)
(c)The x-coordinate is negative.(1)
(d)The y-coordinate is negative.(1)
(Total for Question 7 is 4 marks)
8
Point J is at (3, 5) and point K is at (3, -2). J and K lie on the same vertical gridline. Work out the vertical distance between J and K.
(Total for Question 8 is 2 marks)
9
On a treasure map, positions are given as coordinates (across, up) on a grid. The chest is at (2, 3). The key is 5 units to the right and 4 units up from the chest.
(a)Work out the coordinates of the key.(2)
(b)The cave entrance lies on the y-axis, 6 units above the origin. Write down the coordinates of the cave entrance.(1)
(Total for Question 9 is 3 marks)
10
Point M is at (-2, 4). Point N is 5 units to the right and 3 units down from M. Work out the coordinates of N.
(Total for Question 10 is 2 marks)
11
ABCD is a rectangle drawn on a coordinate grid, with sides parallel to the axes. A = (1, 2), B = (6, 2), C = (6, 5). Find the coordinates of D.
(Total for Question 11 is 2 marks)
12
PQRS is a square drawn on a coordinate grid, with sides parallel to the axes. P = (-4, -1), Q = (2, -1), R = (2, 5). Find the coordinates of S.
Diagram NOT accurately drawn
(Total for Question 12 is 3 marks)
13
Four points are plotted on a coordinate grid: W(-3, 2), X(1, 2), Y(1, -2) and Z(-3, -2). Write down the mathematical name of the quadrilateral WXYZ. Give a reason for your answer.
Diagram NOT accurately drawn
(Total for Question 13 is 3 marks)
14
Point A is at (5, 3).
(a)Point A is reflected in the x-axis to give point B. Write down the coordinates of B.(1)
(b)Point A is reflected in the y-axis to give point C. Write down the coordinates of C.(1)
(Total for Question 14 is 2 marks)
15
A sequence of points is generated on a grid. The first point is (1, -2). Each new point is formed by adding 3 to the x-coordinate and adding 2 to the y-coordinate of the previous point.
(a)Write down the coordinates of the second point in the sequence.(1)
(b)Write down the coordinates of the third point in the sequence.(1)
(c)One of the points in the sequence has coordinates (16, y). Work out the value of y.(2)
(Total for Question 15 is 4 marks)
16
Kwame says: 'The point (-2, 0) lies on the x-axis because the x-coordinate is negative.' Kwame's reasoning is incorrect. Explain why.
(Total for Question 16 is 2 marks)
17
A rectangular garden is drawn on a coordinate grid, where 1 unit represents 1 metre. Three corners of the garden are at (1, 1), (9, 1) and (9, 6).
Diagram NOT accurately drawn
(a)Find the coordinates of the fourth corner of the garden.(2)
(b)Work out the perimeter of the garden.(2)
(Total for Question 17 is 4 marks)
18
A robot starts at point (-4, -3) on a grid, where each unit represents 1 metre.
(a)The robot moves 6 metres to the right and 5 metres up to reach point R. Work out the coordinates of R.(2)
(b)The robot then moves in a straight vertical line from R to point S(2, -6). Work out the distance the robot moves from R to S.(2)
(Total for Question 18 is 4 marks)
Mark scheme · 1.12 Coordinates
Question 1
(a) B1 (2, 5) cao
(a) Answer: (2, 5)
(b) B1 (6, 1) cao
(b) Answer: (6, 1)
(c) B1 (0, 4) cao
(c) Answer: (0, 4)
(d) B1 (7, 0) cao
(d) Answer: (7, 0)
Question 2
(a) B1 point plotted at (3, 7), labelled E
(a) Answer: Point plotted 3 across, 7 up
(b) B1 point plotted at (9, 2), labelled F
(b) Answer: Point plotted 9 across, 2 up
(c) B1 point plotted at (0, 6), labelled G, on the y-axis
(c) Answer: Point plotted on the y-axis, 6 up
(d) B1 point plotted at (5, 0), labelled H, on the x-axis
(d) Answer: Point plotted on the x-axis, 5 across
Question 3
(a) B1 (0, 0) cao
(a) Answer: (0, 0)
(b) B1 (0, 5) cao
(b) Answer: (0, 5)
Question 4
(a) B1 (-3, 4) cao
(a) Answer: (-3, 4)
(b) B1 (5, -2) cao
(b) Answer: (5, -2)
(c) B1 (-4, -5) cao
(c) Answer: (-4, -5)
(d) B1 (3, 6) cao
(d) Answer: (3, 6)
Question 5
(a) B1 point plotted at (-5, -3), labelled T
(a) Answer: Point plotted 5 left, 3 down
(b) B1 point plotted at (4, 5), labelled U
(b) Answer: Point plotted 4 right, 5 up
(c) B1 point plotted at (-2, 6), labelled V
(c) Answer: Point plotted 2 left, 6 up
(d) B1 point plotted at (6, -4), labelled W
(d) Answer: Point plotted 6 right, 4 down
Question 6
(a) B1 top-left cao
(a) Answer: Top-left
(b) B1 bottom-right cao
(b) Answer: Bottom-right
(c) B1 bottom-left cao
(c) Answer: Bottom-left
Question 7
(a) B1 True cao
(a) Answer: True
(b) B1 False cao
(b) Answer: False
(c) B1 True cao
(c) Answer: True
(d) B1 False cao
(d) Answer: False
Question 8
M1 correct method, e.g. 5 - (-2) oe, or squares counted correctly
A1 7 (units) cao
Answer: 7 units
Question 9
(a) M1 correct method, e.g. 2 + 5 and/or 3 + 4
(a) A1 (7, 7) cao
(a) Answer: (7, 7)
(b) B1 (0, 6) cao
(b) Answer: (0, 6)
Question 10
M1 correct method, e.g. -2 + 5 and/or 4 - 3
A1 (3, 1) cao
Answer: (3, 1)
Question 11
M1 recognising D has the same x-coordinate as A and the same y-coordinate as C, oe
A1 (1, 5) cao
Answer: (1, 5)
Question 12
M1 side length of the square found, e.g. PQ = 6 or QR = 6, oe
M1 correct method for S, e.g. same x-coordinate as P and same y-coordinate as R
A1 (-4, 5) cao
Answer: (-4, 5)
Question 13
M1 at least two correct side lengths found, e.g. WX = 4 and XY = 4
A1 correct reasoning that all four sides are equal length and all angles are right angles, oe (ft from M1)
B1 square cao
Answer: Square (all four sides have length 4 units and all angles are 90 degrees)
Question 14
(a) B1 (5, -3) cao
(a) Answer: (5, -3)
(b) B1 (-5, 3) cao
(b) Answer: (-5, 3)
Question 15
(a) B1 (4, 0) cao
(a) Answer: (4, 0)
(b) B1 (7, 2) cao
(b) Answer: (7, 2)
(c) M1 correct method to find which term has x = 16, e.g. 1 + 3n = 16 so n = 5, oe
(c) A1 y = 8 cao
(c) Answer: y = 8
Question 16
B1 correctly identifies that the point does lie on the x-axis, but for the wrong reason: it is because the y-coordinate is 0
B1 valid supporting explanation/counter-example that the sign of the x-coordinate does not determine whether a point is on the x-axis, e.g. (3, 0) also lies on the x-axis despite having a positive x-coordinate
Answer: The point does lie on the x-axis, but this is because its y-coordinate is 0, not because the x-coordinate is negative. Any point with y = 0 lies on the x-axis, whatever the sign of x.
Question 17
(a) M1 recognising the fourth corner shares an x-coordinate with (1,1) and a y-coordinate with (9,6), oe