2E - The midpoint of a line

Learning intentions:

In this section we will examine:

    • How determine the midpoint of a line segment.

The midpoint of a line segment

When a line is drawn between the points A(x1, y1) and B(x2, y2), the midpoint is the point on the line which bisects A and B (divides A and B in half). Essentially, the midpoint will be half way between the two given x-values and the two corresponding y-values. Therefore:

MAKE DIAGRAM

Finding the midpoint given two endpoints

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2E - EXAMPLE 1:

What are the coordinates of the midpoint between the points (2,7) and (8,19)?

Finding an endpoint given the midpoint and an endpoint

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Further applications of midpoints

Finding the coordinates that divide a line in 3 equal segments.

RESOURCES

  • http://www.onlinemathlearning.com/midpoint-formula.html
  • http://www.bbc.co.uk/schools/gcsebitesize/maths/geometry/linesegmentsrev2.shtml
  • http://www.regentsprep.org/regents/math/geometry/gcg2/pracMid.htm
  • http://www.mathwarehouse.com/geometry/interactive-midpoint-applet.php
  • https://www.mathsisfun.com/algebra/line-midpoint.html
  • http://www.cimt.plymouth.ac.uk/projects/mepres/allgcse/add_13.2c.pdf

Success criteria:

You will be successful if you can:

  1. Calculate the midpoint of a line segment.
  2. Apply knowledge of the midpoint formula to unfamiliar contexts.