Coordinates in four quadrants - Edexcel GCSE Maths (Non-calculator) Exam Questions

Practise 19 exam-style questions on Coordinates in four quadrants for Edexcel GCSE Maths (Non-calculator). Write your answer as you would in the exam and get it marked in seconds against the mark scheme, point by point, with an AI tutor on hand if you get stuck.

19 questions
1–5 marks each
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19 questions, marked as you go

Sample questions with model answers

Here are 4 of the questions in this topic, each with a model answer, an explanation of why it earns the marks and the mark scheme an examiner would use.

Question 1

2 marks

A is the point \((-3, 4)\) and B is the point \((5, -2)\).

Work out the coordinates of the midpoint of AB.

Model answer

\(x = \dfrac{-3 + 5}{2} = \dfrac{2}{2} = 1\)
\(y = \dfrac{4 + (-2)}{2} = \dfrac{2}{2} = 1\)
Midpoint \(= (1, 1)\)

Explanation

The midpoint is the mean of the two \(x\)-coordinates and the mean of the two \(y\)-coordinates. Add the coordinates and halve - take care with the negative numbers.

Mark scheme

1 mark
M1 for \(\dfrac{-3 + 5}{2}\) or \(\dfrac{4 + (-2)}{2}\)
or one correct coordinate; correct answer with no working scores full marks
1 mark
A1 for \((1, 1)\)
cao

Question 2

2 marks

The points \((-1, 2)\), \((5, 2)\) and \((5, -4)\) are three of the vertices of a square.

Work out the coordinates of the centre of the square.

Model answer

\((-1, 2)\) and \((5, -4)\) are opposite corners (the ends of a diagonal).
Centre \(= \left(\dfrac{-1 + 5}{2}, \dfrac{2 + (-4)}{2}\right) = (2, -1)\)

Explanation

The diagonals of a square cross at its centre, and each diagonal is bisected there. So the centre is the midpoint of the two opposite vertices. The points \((-1, 2)\) and \((5, -4)\) are opposite because they differ in both coordinates.

Mark scheme

1 mark
M1 for a correct method, e.g. the midpoint of \((-1, 2)\) and \((5, -4)\), or finding the fourth vertex \((-1, -4)\) and then a midpoint of a diagonal
or one correct coordinate; correct answer with no working scores full marks
1 mark
A1 for \((2, -1)\)
cao

Question 3

3 marks

The points A\((-3, -4)\), B\((1, 2)\) and C\((9, k)\) lie on a straight line.

Work out the value of \(k\).

Model answer

From A to B: 4 across and 6 up.
From B to C: \(9 - 1 = 8\) across, which is 2 lots of 4.
So it must go 2 lots of 6 = 12 up.
\(k = 2 + 12 = 14\)

Explanation

Points on a straight line go up by the same amount for each unit across. Since B to C is twice as far across as A to B, it must also be twice as far up. Using gradients: \(\dfrac{6}{4} = \dfrac{k - 2}{8}\) gives the same result.

Mark scheme

1 mark
P1 for the step from A to B, 4 across and 6 up, or the gradient \(\dfrac{6}{4}\)
oe, e.g. \(\dfrac{3}{2}\); correct answer with no working scores full marks
1 mark
P1 for recognising that B to C is 8 across, so 12 up, or for \(\dfrac{k - 2}{8} = \dfrac{3}{2}\)
1 mark
A1 for \(k = 14\)
cao

Question 4

4 marks

Three vertices of a parallelogram are \((-2, 1)\), \((3, 2)\) and \((1, -3)\).

Work out the coordinates of all three possible positions of the fourth vertex.

Model answer

Call the points P\((-2, 1)\), Q\((3, 2)\), R\((1, -3)\). The fourth vertex completes a parallelogram with any one of the three points opposite it.
Opposite R: \(P + Q - R = (-2 + 3 - 1, 1 + 2 + 3) = (0, 6)\)
Opposite Q: \(P + R - Q = (-2 + 1 - 3, 1 - 3 - 2) = (-4, -4)\)
Opposite P: \(Q + R - P = (3 + 1 + 2, 2 - 3 - 1) = (6, -2)\)
The fourth vertex could be \((0, 6)\), \((-4, -4)\) or \((6, -2)\).

Explanation

The question does not say which vertices are next to each other, so each of the three given points could be opposite the missing one. In a parallelogram, the same step that takes one vertex to its neighbour takes the opposite vertex to its neighbour. Check one: from \((1, -3)\) to \((3, 2)\) is 2 right, 5 up, and from \((-2, 1)\) the same step reaches \((0, 6)\).

Mark scheme

1 mark
P1 for a correct method for one position, e.g. using the step between two vertices from the third vertex
correct answer with no working scores full marks
1 mark
B1 for one correct position
positions: (0, 6), (−4, −4), (6, −2)
1 mark
B1 for a second correct position
1 mark
B1 for the third correct position
deduct this mark if any incorrect position is also given

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