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Cambridge IGCSE0607

Coordinates

International Mathematics 0607 Chapter Notes

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Coordinates
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Coordinates notes

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In this chapter

  1. 1Writing a point as (x, y)
  2. 2Negative coordinates
  3. 3Points on a line and on an axis

1. Writing a point as (x, y)

A point in two dimensions is fixed by two Cartesian coordinates, written in brackets as (x, y). The x-coordinate comes first. It says how far the point is along the horizontal x-axis.

The y-coordinate comes second. It says how far the point is up the vertical y-axis.

Examiner insight

“A small number wrote the values the wrong way round, i.e. (y, x).”

Worked example 12 marks

The diagram shows triangle PQR drawn on a grid.

(a) Write down the coordinates of R.

(b) Write down the letter of the point with the same x-coordinate as Q.

  1. 1

    R is 6 across and 4 up, so R = (6, 4) [1]

  2. 2

    Q is at (6, 1). R also has x-coordinate 6, so the point is R [1]

2. Negative coordinates

A point to the left of the y-axis has a negative x-coordinate. A point below the x-axis has a negative y-coordinate.

Read the sign with the number. The point (1, -1) is 1 to the right of the y-axis and 1 below the x-axis.

Examiner insight

“Surprisingly a lot of answers were spoilt by the omission of a negative sign in the y-coordinate.”

Worked example 11 mark

Point M is 3 units left of the y-axis and 2 units below the x-axis. Write down the coordinates of M.

  1. 1

    left of the y-axis, so x = -3; below the x-axis, so y = -2

  2. 2

    M = (-3, -2) [1]

3. Points on a line and on an axis

Points on the same vertical line have the same x-coordinate. Points on the same horizontal line have the same y-coordinate.

A point on the x-axis has y-coordinate 0. A point on the y-axis has x-coordinate 0. The axes cross at the origin, (0, 0).

Examiner insight

“A few did not appear to realise that the y-coordinate is zero so gave (1, 3) as their answer.”

Worked example 12 marks

Three corners of rectangle ABCD are A(2, 1), B(2, 6) and C(7, 6). Write down the coordinates of D.

  1. 1

    AB is vertical and BC is horizontal. CD is vertical, so D has the same x-coordinate as C: 7 [1]

  2. 2

    DA is horizontal, so D has the same y-coordinate as A: 1. D = (7, 1) [1]

Recap

  • A point is written (x, y): the x-coordinate first, the y-coordinate second.
  • The origin is (0, 0).
  • Left of the y-axis, x is negative. Below the x-axis, y is negative.
  • Same vertical line, same x. Same horizontal line, same y.
  • On the x-axis, y is 0. On the y-axis, x is 0.

End-of-chapter exercise

Test yourself on the whole chapter. Work through these before moving on.

  1. Write down the coordinates of the origin.1 mark
  2. Point P is 4 units to the right of the y-axis and 7 units above the x-axis. Write down the coordinates of P.1 mark
  3. Triangle ABC has corners A(1, 2), B(6, 2) and C(3, 5). (a) Write down the y-coordinate of C. (b) Write down the letter of the corner with the same y-coordinate as A.2 marks
  4. Do not use a calculator. Point Q has coordinates (-3, 5). State how many units Q is to the left or right of the y-axis, and how many units above or below the x-axis.2 marks
  5. Write down the coordinates of a point on the x-axis that is 5 units to the left of the origin.1 mark
  6. Do not use a calculator. Three corners of rectangle ABCD are A(-2, 1), B(-2, 6) and C(4, 6). Write down the coordinates of D.2 marks
  7. Do not use a calculator. Points P(-4, 3) and Q(5, 3) lie on the same horizontal line. How many units apart are they?2 marks
  8. Do not use a calculator. Point L has coordinates (-4, 2). Point M has the same y-coordinate as L. The x-coordinate of M is 6 more than the x-coordinate of L. Write down the coordinates of M.2 marks
  9. A computer game shows four markers at A(-4, 0), B(2, 3), C(1, -1) and D(2, -3). (a) The x-coordinate of B is 6 more than the x-coordinate of one of the other markers. Write down the letter of this marker. (b) A fifth marker E has the same x-coordinate as C. The y-coordinate of E is 5 less than the y-coordinate of B. Write down the coordinates of E.4 marks
  10. Do not use a calculator. On a plan of a field, east is the positive x direction and north is the positive y direction. Two posts are at A(-3, -4) and B(5, -4). ABCD is a rectangle with C north of B. The side BC is 6 units long. (a) Write down the coordinates of C and of D. (b) A gate G is at the point where side CD crosses the y-axis. Write down the coordinates of G. (c) A tap T is on side AB. The x-coordinate of T is 6 more than the x-coordinate of A. Find how many units T is from B.5 marks

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