Maths Essentials, Unit 27, Lesson 2 of 4

Vectors between points

GCSE Maths, Vectors, 20 minutes

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The vector from A to B, joining vectors end to end, parallel vectors and midpoints.

What you will learn

  • Find the vector AB from the coordinates of A and B
  • Join vectors end to end
  • Recognise and use parallel vectors
  • Find a midpoint with vectors

From A to B

The vector AB takes you from A to B, so subtract: AB = B − A, row by row.

BA goes the other way, so BA = −AB.

  1. A(2, −1) and B(7, 3)
  2. AB: top 7 − 2 = 5, bottom 3 − (−1) = 4
  3. BA: top −5, bottom −4

Going the other way, a point plus a vector gives a new point: B = A + AB. From A(1, 2) with AB = (4, −3) as a column, B is (5, −1). For a point C with AC = 2 × AB, find AC = (8, −6) first, then C = (1 + 8, 2 − 6) = (9, −4).

With O the origin, the vector OA (the position vector of A) has the same numbers as the coordinates of A, so AB = OB − OA. The midpoint M of AB is halfway along: OM = OA + ½AB. With OA = (2, 6) and OB = (8, 0), AB = (6, −6), ½AB = (3, −3) and OM = (5, 3).

The rest of this lesson and its 8 practice questions are locked.

In this lesson

  1. From A to B
  2. Routes and parallel vectors
  3. Try it: First question

8 practice questions, marked as you go; about 20 minutes in all.

Key terms

Position vector, Equal, Parallel

In this unit: Vectors

Column vectors and how to add, subtract and multiply them, vectors between points, and vector geometry and proof in terms of a and b.

All of Vectors

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