Coordinates Worked Solutions — GCSE Maths

Fully worked, step-by-step solutions to GCSE Coordinates questions. See exactly how to solve problems on reading coordinates, four quadrants, reasoning, midpoint.

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.

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 BB. Write down the coordinates of BB.

Worked solution

  1. Read across to find the x-coordinate

    x=−3x = -3

    Start at the origin and count left along the x-axis to point B. This gives x=−3x = -3.

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

    y=2y = 2

    From point B read across to the y-axis, counting up. This gives y=2y = 2.

  3. Write the coordinates as an ordered pair

    (−3,2)(-3, 2)

    Always write coordinates as (x, y). Point B is in the second region, so its coordinates are (-3, 2).

Answer
(−3,2)(-3, 2)
Question 3
1 markeasy
The grid shows point CC. Write down the coordinates of CC.

Worked solution

  1. Read across to find the x-coordinate

    x=−2x = -2

    Start at the origin and count left along the x-axis to point C. This gives x=−2x = -2.

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

    y=−4y = -4

    From point C read across to the y-axis, counting down. This gives y=−4y = -4.

  3. Write the coordinates as an ordered pair

    (−2,−4)(-2, -4)

    Always write coordinates as (x, y). Point C is in the third region, so its coordinates are (-2, -4).

Answer
(−2,−4)(-2, -4)
Question 4
1 markeasy
The grid shows point DD. Write down the coordinates of DD.

Worked solution

  1. Read across to find the x-coordinate

    x=5x = 5

    Start at the origin and count right along the x-axis to point D. This gives x=5x = 5.

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

    y=−1y = -1

    From point D read across to the y-axis, counting down. This gives y=−1y = -1.

  3. Write the coordinates as an ordered pair

    (5,−1)(5, -1)

    Always write coordinates as (x, y). Point D is in the fourth region, so its coordinates are (5, -1).

Answer
(5,−1)(5, -1)
Question 5
1 markeasy
In which quadrant does the point (−6,3)(-6, 3) lie?

Worked solution

  1. Check the sign of the x-coordinate

    x=−6x = -6\;(negative)

    A negative x means the point is to the left of the y-axis.

  2. Check the sign of the y-coordinate

    y=3y = 3\;(positive)

    A positive y means the point is above the x-axis.

  3. Combine the signs to name the quadrant

    (−, +)(-,\,+)

    Quadrants are numbered anticlockwise from the top right. This sign pair places the point in the second quadrant.

Answer
The second quadrant

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