Collinearity - Rectilinear Shapes - Higher Maths Revision - BBC

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In this guide

  1. Revise
  2. Test
  1. Basics of straight lines
  2. Equation of a straight line
  3. Parallel lines
  4. Perpendicular lines
  5. Collinearity
  6. Equation of medians and parallel lines
  7. Point of intersection
  8. Medians, altitudes and perpendicular bisectors
  9. Equation of altitudes and perpendicular bisectors
  10. Worked example

Collinearity

Three or more points are said to be collinear if they all lie on the same straight line.

Collinear lines mAB and mBC share point B

If A, B and C are collinear then \({m_{AB}} = {m_{BC}}( = {m_{AC}})\) .

If you want to show that three points are collinear, choose two line segments, for example \(AB\) and \(BC\). You then need to establish that they have:

  • a common direction (that is, equal gradients)
  • a common point (for example, B)

If both of these statements are true then the points are collinear.

Example

Show that \(P(1,4)\), \(Q(4,6)\) and \(R(10,10)\) are collinear.

Solution

For this example we'll use the lines PQ and PR.

\({m_{PQ}} = \frac{{6 - 4}}{{4 - 1}} = \frac{2}{3}\)

\({m_{PR}} = \frac{{10 - 4}}{{10 - 1}} = \frac{6}{9} = \frac{2}{3}\)

The line segments have a common direction (gradients \(= \frac{2}{3}\)) and a common point \((P)\) so \(P\), \(Q\) and \(R\) are collinear.

Next pageEquation of medians and parallel linesPrevious pagePerpendicular lines

More guides on this topic

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  • Sequences

Related links

  • BBC Podcasts: Maths
  • BBC Radio 4: Maths collection
  • SQA: Higher Mathematics
  • Emaths
  • Stemnet
  • NRICH

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