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IGCSE Maths: Coordinate geometry

Topic 3 of the Cambridge IGCSE Mathematics (0580) syllabus: coordinates, gradients, midpoints and the equations of straight lines. Here is what each part asks, a practice question for each, and the mistakes that cost the most marks.

Practise coordinate geometry as a game

The 7 parts of the topic

Each part with one practice question, made by the same engine your child plays. Parts marked Extended are for the Extended paper only.

3.1 Coordinates in two dimensions

The questions for this part come with a picture or are played as a game, so they are best tried in Huh Lab.

3.2 Drawing linear graphs

A point on the line x + y = 3 has x = 3.
What are its coordinates?

  1. (3, 5)
  2. (3, 0)
  3. (0, 3)
  4. (3, −6)
Show the answer

(3, 0). Put x = 3 into the equation: y = 0. The point is (3, 0): x first, then y.

3.3 Gradient of a line

Find the gradient of the line through
(−2, 0) and (3, −4).

  1. −4/5
  2. 5/4
  3. −5/4
  4. 4/5
Show the answer

−4/5. Change in y ÷ change in x = −4 ÷ 5 = −4/5.

3.4 Length and midpoint of a line segment Extended

Find the midpoint of
(3, −1) and (−1, 7).

  1. (2, 6)
  2. (1, 3)
  3. (3, 1)
  4. (−2, 4)
Show the answer

(1, 3). Average the x values and the y values: (1, 3).

3.5 Equations of lines: y = mx + c, and the line through two points

Find the equation of the line through (−3, −13) and (−2, −8).

  1. y = −5x + 2
  2. y = 5x + 2
  3. y = 2x + 5
  4. y = 5x − 13
Show the answer

y = 5x + 2. Gradient = (−8 − −13) ÷ (−2 − −3) = 5. Put one point in y = 5x + c to find c = 2.

3.6 Parallel lines

A line is parallel to y = 6x − 7
and passes through (0, −1). Find its equation.

  1. y = 6x − 7
  2. y = 6x + 1
  3. y = −6x − 1
  4. y = 6x − 1
Show the answer

y = 6x − 1. Parallel lines have the SAME gradient, 6. Put (0, −1) in y = 6x + c: −1 = 0 + c, so c = −1.

3.7 Perpendicular lines Extended

A line has equation
y = 2x + 1
What is the gradient of a line perpendicular to it?

  1. −1/2
  2. 2
  3. −2
  4. 1/2
Show the answer

−1/2. Its gradient is 2. Perpendicular gradients multiply to −1: flip it AND change the sign, giving −1/2.

The mistakes that cost the most marks

Huh Lab checks every wrong answer against known mistakes like these, and goes back to the step behind the one your child keeps making.

Gives the y-coordinate first

Along the corridor, THEN up the stairs: x comes before y.

Only flips, or only changes the sign

A perpendicular gradient needs BOTH: turn the fraction upside down and change its sign.

Swaps the gradient and the intercept

In y = mx + c, m is how STEEP the line is and c is where it crosses the y-axis.

Changes the gradient of a parallel line

Parallel lines never meet because they are equally steep: same gradient, different c.

Loses the negative sign

Use a number line: below zero the numbers keep counting, in the other direction.

Other IGCSE Maths topics

Number17 parts Algebra and graphs13 parts Geometry8 parts Mensuration5 parts Trigonometry6 parts Transformations and vectors4 parts Probability4 parts Statistics7 parts

Practise it as a game

Short rounds on any topic, a new question every time, the exact mistake found, and a report to you after every session.

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