GCSE Coordinates Practice Questions

Free GCSE Coordinates practice questions with full step-by-step worked solutions. Covers reading coordinates, four quadrants, reasoning, midpoint. Practise exam-style problems and check your method.

reading coordinatesfour quadrantsreasoningmidpointaverage of coordinateslength
GCSE Foundation70 questionsStep-by-step solutions
Question 1
1 markeasy
The grid shows point AA. Write down the coordinates of AA.
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Worked solution

  1. Read across to find the x-coordinate

    x=4x = 4

    Start at the origin and count right along the x-axis to point A. This gives x=4x = 4.

  2. Read up or down to find the y-coordinate

    y=3y = 3

    From point A read across to the y-axis, counting up. This gives y=3y = 3.

  3. Write the coordinates as an ordered pair

    (4,3)(4, 3)

    Always write coordinates as (x, y). Point A is in the first region, so its coordinates are (4, 3).

Answer
(4,3)(4, 3)
Question 2
1 markeasy
The grid shows point QQ, which lies on an axis. Write down the coordinates of QQ.
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Worked solution

  1. Read across to find the x-coordinate

    x=−5x = -5

    Start at the origin and count left along the x-axis to point Q. This gives x=−5x = -5.

  2. Read up or down to find the y-coordinate

    y=0y = 0

    From point Q read across to the y-axis, counting up. This gives y=0y = 0.

  3. Write the coordinates as an ordered pair

    (−5,0)(-5, 0)

    Always write coordinates as (x, y). Point Q is in the x-axis region, so its coordinates are (-5, 0).

Answer
(−5,0)(-5, 0)
Question 3
2 marksintermediate
Find the midpoint of the segment joining (−4,5)(-4, 5) and (8,−1)(8, -1).
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Worked solution

  1. Label the two points

    A=(−4,5),B=(8,−1)A = (-4, 5), \quad B = (8, -1)

    Name the endpoints so it is clear which numbers are x-values and which are y-values.

  2. Write down the midpoint formula

    M=(x1+x22,y1+y22)M = \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)

    The midpoint is the mean of the endpoints' coordinates.

  3. Substitute into the formula

    M=(−4+82,5+−12)M = \left(\frac{-4+8}{2}, \frac{5+-1}{2}\right)

    Substitute carefully, watching the signs of any negative coordinates.

  4. Work out the x-coordinate

    x=42=2x = \frac{4}{2} = 2

    Add the x-values -4 and 8, then halve to get 2.

  5. Work out the y-coordinate

    y=42=2y = \frac{4}{2} = 2

    Add the y-values 5 and -1, then halve to get 2.

  6. State the midpoint

    M=(2,2)M = (2, 2)

    The midpoint of AB is (2, 2).

Answer
(2,2)(2, 2)
Question 4
4 markshard
A triangle has vertices A=(0,0)A=(0, 0), B=(9,0)B=(9, 0) and C=(9,12)C=(9, 12). Work out the perimeter of the triangle.
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Worked solution

  1. List the vertices of the triangle

    A=(0,0),  B=(9,0),  C=(9,12)A=(0, 0),\; B=(9, 0),\; C=(9, 12)

    The perimeter is the sum of the three side lengths.

  2. Set up the distance formula

    d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

    Use it for each side in turn.

  3. Length of AB

    AB=(9)2+(0)2=81=9AB = \sqrt{(9)^2+(0)^2} = \sqrt{81} = 9

    Square the horizontal and vertical gaps, add, then square-root.

  4. Length of BC

    BC=(0)2+(12)2=144=12BC = \sqrt{(0)^2+(12)^2} = \sqrt{144} = 12

    Repeat for the side BC.

  5. Length of CA

    CA=(−9)2+(−12)2=225=15CA = \sqrt{(-9)^2+(-12)^2} = \sqrt{225} = 15

    And once more for CA.

  6. Add the three sides

    P=9+12+15P = 9 + 12 + 15

    The perimeter is the total of the side lengths.

  7. Simplify the perimeter

    P=36P = 36

    Add the whole numbers to get the perimeter.

  8. Classify the triangle

    all sides differ

    All three sides differ, so the triangle is scalene.

  9. Sketch check

    plot A,B,C\text{plot } A,B,C

    Plotting the points confirms the side lengths look right relative to the grid.

  10. State the perimeter

    P=36P = 36

    The perimeter of triangle ABC is 36 units.

Answer
3636
Question 5
5 markschallenging
A=(1,2)A=(1, 2), B=(1,7)B=(1, 7), C=(10,7)C=(10, 7) and D=(10,2)D=(10, 2) are the vertices of rectangle ABCDABCD. Work out its area and perimeter.
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Worked solution

  1. List the four vertices

    A=(1,2),  B=(1,7),  C=(10,7),  D=(10,2)A=(1, 2),\; B=(1, 7),\; C=(10, 7),\; D=(10, 2)

    We confirm ABCD is a rectangle and find its area and perimeter.

  2. Vector AB

    AB⃗=(0,5)\vec{AB} = (0, 5)

    Find the direction and length of side AB.

  3. Length of AB

    AB=(0)2+(5)2=5AB = \sqrt{(0)^2+(5)^2} = 5

    Side AB is 5 units long.

  4. Vector BC

    BC⃗=(9,0)\vec{BC} = (9, 0)

    Find the direction and length of side BC.

  5. Length of BC

    BC=(9)2+(0)2=9BC = \sqrt{(9)^2+(0)^2} = 9

    Side BC is 9 units long.

  6. Check the corner is a right angle

    AB⃗⋅BC⃗=0\vec{AB} \cdot \vec{BC} = 0

    The two side vectors are perpendicular, confirming a rectangle.

  7. Check the fourth vertex

    D=A+BC⃗=(10,2)D = A + \vec{BC} = (10, 2)

    D completes the rectangle as given.

  8. Write the area formula

    Area=length×width\text{Area} = \text{length} \times \text{width}

    For a rectangle, multiply the two different side lengths.

  9. Substitute the side lengths

    Area=5×9\text{Area} = 5 \times 9

    Use AB and BC as the length and width.

  10. Work out the area

    Area=45\text{Area} = 45

    The area is 45 square units.

  11. Write the perimeter formula

    Perimeter=2(length+width)\text{Perimeter} = 2(\text{length}+\text{width})

    Add the four sides.

  12. Work out the perimeter

    P=2(5+9)=28P = 2(5+9) = 28

    The perimeter is 28 units.

  13. Sketch check

    plot A,B,C,D\text{plot } A,B,C,D

    The plotted points form the expected axis-aligned rectangle.

  14. Common mistake

    5+9≠Area5+9 \neq \text{Area}

    Area multiplies the sides; adding them gives half the perimeter, not the area.

  15. State the results

    Area=45,  P=28\text{Area} = 45,\; P = 28

    The rectangle has area 45 square units and perimeter 28 units.

Answer
Area = 45, perimeter = 28

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