Coordinates (Part 2) - Worksheets, Questions and Revision

18 original exam-style questions - 7 pages of questions with a full mark scheme - free printable PDF.

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1.12B Coordinates (Part 2)

EDEXCEL 1MA1 · Calculator allowed · about 60 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Four points are described below. Complete the table by writing down the coordinates of each point.

(a)Point E is 6 units to the right and 3 units up from the origin.(1)

(b)Point F is on the x-axis, 8 units to the left of the origin.(1)

(c)Point G is 4 units to the left and 5 units up from the origin.(1)

(d)Point H is on the y-axis, 7 units below the origin.(1)

(Total for Question 1 is 4 marks)

Each part gives the coordinates of a point. Write down which quadrant (1, 2, 3 or 4) the point lies in. If the point lies on an axis, write 'on an axis' instead of a quadrant number.

(a)(5, -3)(1)

(b)(-6, 2)(1)

(c)(-1, -8)(1)

(d)(0, 4)(1)

(Total for Question 2 is 4 marks)

Point A is at (6, -2). Point A is reflected in the x-axis to give point B. Point B is then reflected in the y-axis to give point C. Work out the coordinates of point C.

(Total for Question 3 is 2 marks)

A student, Erin, says: 'If you translate a point 5 units up and then 5 units down, you always end up back at the point you started with, whatever point you start at.' Decide whether Erin is correct. Justify your answer with an example.

(Total for Question 4 is 2 marks)

A search-and-rescue drone starts at point (-6, 5) on a grid, where each grid unit represents 10 metres.

(a)The drone flies 9 units to the right and 8 units down to hover above point S. Work out the coordinates of S.(2)

(b)The drone then flies in a straight horizontal line from S to point T(-5, -3). Work out the real-world distance flown from S to T, in metres.(2)

(Total for Question 5 is 4 marks)

Three points are plotted on a grid: P(-5, 4), Q(1, 4) and R(8, 4).

(a)Show that P, Q and R lie on a straight horizontal line, and write down the equation of this line.(3)

(b)State whether the point (100, 4) also lies on this line.(1)

(Total for Question 6 is 4 marks)

Find the equation of the straight line that passes through the points (-3, 2) and (-3, 9).

(Total for Question 7 is 2 marks)

Point U is at (2, 3) and point V is at (8, 11). Work out the coordinates of the midpoint of the line segment UV.

(Total for Question 8 is 2 marks)

The midpoint of the line segment WX is (4, -1). Point W is at (-2, 5). Work out the coordinates of point X.

(Total for Question 9 is 3 marks)

KLMN is a parallelogram. K = (-3, 1), L = (2, 1), M = (5, 6). The diagonals of a parallelogram bisect each other.

(a)Work out the coordinates of N.(3)

(b)Show that side KL is parallel to side NM.(1)

(Total for Question 10 is 4 marks)

Answer the following questions about coordinates.

(a)Circle the letter of the point that lies in the fourth quadrant.
A) (-3, 5) B) (4, -6) C) (-2, -7) D) (0, 8)(1)

A) (-3, 5)
B) (4, -6)
C) (-2, -7)
D) (0, 8)

(b)Circle the letter of the point that lies exactly on the x-axis.
A) (0, -5) B) (5, 0) C) (-5, 5) D) (5, 5)(1)

A) (0, -5)
B) (5, 0)
C) (-5, 5)
D) (5, 5)

(Total for Question 11 is 2 marks)

A pupil, Yusuf, was asked to write down the coordinates of the point that is 5 units to the left of the y-axis and 3 units below the x-axis. Yusuf wrote (5, -3).

(a)Explain the mistake Yusuf has made.(2)

(b)Write down the correct coordinates.(1)

(Total for Question 12 is 3 marks)

A coach travels in a straight line from the school, at (-8, 2), to a service station at (10, 2), where each grid unit represents 4 kilometres.

(a)The coach stops for a break exactly halfway between the school and the service station. Work out the coordinates of the stopping point.(2)

(b)Work out the total distance, in kilometres, from the school to the service station.(2)

(c)The coach then continues in a straight vertical line from the service station at (10, 2) to the final destination at (10, -9). Work out the distance travelled from the service station to the final destination, in kilometres.(2)

(Total for Question 13 is 6 marks)

Point Y is at (3, -5). Point Y is reflected in the x-axis to give point Z. Work out the distance YZ.

(Total for Question 14 is 2 marks)

Answer the following questions, where each point has one coordinate given as a letter.

(a)The point (k, 7) lies on the same vertical line as the point (3, -2). Write down the value of k.(1)

(b)The point (5, m) lies on the same horizontal line as the point (-9, 12). Write down the value of m.(1)

(c)The point (2k, 9) lies on the same vertical line as the point (-8, 1). Work out the value of k.(2)

(Total for Question 15 is 4 marks)

A stage designer places props on a grid marked out on the floor of a school hall, where the corner of the hall is the origin.

(a)The piano is placed 7 units from the left wall and 3 units from the front wall. Write down the coordinates of the piano.(1)

(b)The microphone stand is placed on the front-wall line (the x-axis), 4 units to the left of the corner. Write down the coordinates of the microphone stand.(1)

(Total for Question 16 is 2 marks)

Point J is at (6, 2). For each point below, state whether it is above, below, to the left of, or to the right of point J.

(a)(6, 9)(1)

(b)(2, 2)(1)

(c)(6, -3)(1)

(d)(11, 2)(1)

(Total for Question 17 is 4 marks)

A vertical line has the equation x = 4. A horizontal line has the equation y = -3. Write down the coordinates of the point where these two lines cross.

(Total for Question 18 is 2 marks)

Mark scheme · 1.12B Coordinates (Part 2)

Question 1

(a) B1 (6, 3) cao
(a) Answer: (6, 3)
(b) B1 (-8, 0) cao
(b) Answer: (-8, 0)
(c) B1 (-4, 5) cao
(c) Answer: (-4, 5)
(d) B1 (0, -7) cao
(d) Answer: (0, -7)

Question 2

(a) B1 quadrant 4 cao
(a) Answer: Quadrant 4
(b) B1 quadrant 2 cao
(b) Answer: Quadrant 2
(c) B1 quadrant 3 cao
(c) Answer: Quadrant 3
(d) B1 on an axis cao (the y-axis)
(d) Answer: On an axis (the y-axis)

Question 3

M1 reflecting A in the x-axis correctly, e.g. B = (6, 2) seen
A1 (-6, 2) cao, ft their B if M1 awarded
Answer: (-6, 2)

Question 4

B1 correct cao
B1 valid example showing the point returns to its start, e.g. starting at (2, 3): 5 up gives (2, 8), then 5 down gives (2, 3)
Answer: Erin is correct. For example, starting at (2, 3): 5 up gives (2, 8), then 5 down from (2, 8) gives (2, 3), the original point.

Question 5

(a) M1 correct method, e.g. -6 + 9 and/or 5 - 8
(a) A1 (3, -3) cao
(a) Answer: (3, -3)
(b) M1 correct method using their value of S, e.g. their Sx - (-5), oe, ft
(b) A1 80 metres cao (dep on a correct S)
(b) Answer: 80 metres

Question 6

(a) B1 P, Q and R all have y-coordinate 4
(a) B1 points with the same y-coordinate lie on a horizontal line, oe, so P, Q and R are collinear
(a) B1 y = 4 cao
(a) Answer: P, Q and R are collinear because they all have y-coordinate 4; the line is y = 4.
(b) B1 yes, oe, because its y-coordinate is 4
(b) Answer: Yes

Question 7

M1 recognising both points have the same x-coordinate, oe
A1 x = -3 cao
Answer: x = -3

Question 8

M1 correct method, e.g. (2 + 8)/2 and/or (3 + 11)/2
A1 (5, 7) cao
Answer: (5, 7)

Question 9

M1 correct method for the x-coordinate, e.g. 2 x 4 - (-2), oe
M1 correct method for the y-coordinate, e.g. 2 x (-1) - 5, oe
A1 (10, -7) cao
Answer: (10, -7)

Question 10

(a) M1 finding the midpoint of diagonal KM, e.g. ((-3+5)/2, (1+6)/2) = (1, 3.5)
(a) M1 dep on the first M1: setting this equal to the midpoint of LN and forming an equation for N, oe
(a) A1 (0, 6) cao
(a) Answer: (0, 6)
(b) B1 KL and NM are both horizontal (or have the same direction), e.g. K to L is (5, 0) and N to M is (5, 0)
(b) Answer: KL and NM are both horizontal, so they are parallel.

Question 11

(a) B1 B cao
(a) Answer: B
(b) B1 B cao
(b) Answer: B

Question 12

(a) B1 identifies that Yusuf has used a positive x-coordinate
(a) B1 correct reason, e.g. 'to the left of the y-axis' means the x-coordinate should be negative, oe
(a) Answer: Yusuf wrote the x-coordinate as positive 5, but 'to the left of the y-axis' means the x-coordinate should be negative.
(b) B1 (-5, -3) cao
(b) Answer: (-5, -3)

Question 13

(a) M1 correct method, e.g. (-8 + 10)/2 and/or (2 + 2)/2
(a) A1 (1, 2) cao
(a) Answer: (1, 2)
(b) M1 correct method, e.g. 10 - (-8) = 18 (units), oe
(b) A1 72 km cao
(b) Answer: 72 km
(c) M1 correct method, e.g. 2 - (-9) = 11 (units), oe
(c) A1 44 km cao
(c) Answer: 44 km

Question 14

M1 correct reflection, e.g. Z = (3, 5) seen, or correct method for the distance
A1 10 units cao
Answer: 10 units

Question 15

(a) B1 k = 3 cao
(a) Answer: k = 3
(b) B1 m = 12 cao
(b) Answer: m = 12
(c) M1 correct equation, e.g. 2k = -8, oe
(c) A1 k = -4 cao
(c) Answer: k = -4

Question 16

(a) B1 (7, 3) cao
(a) Answer: (7, 3)
(b) B1 (-4, 0) cao
(b) Answer: (-4, 0)

Question 17

(a) B1 above cao
(a) Answer: Above
(b) B1 to the left cao
(b) Answer: To the left
(c) B1 below cao
(c) Answer: Below
(d) B1 to the right cao
(d) Answer: To the right

Question 18

B1 x-coordinate 4 identified
B1 (4, -3) cao
Answer: (4, -3)

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Coordinates (Part 2) - Worksheets, Questions and Revision

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1.12B Coordinates (Part 2)

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Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18