“Teach A Level Maths” Vol. 1: AS Core Modules 2: Mid-Point and Length of Line © Christine Crisp

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The mid-point is the average of the end points: M X The mid-point is the average of the end points:

A formula for the Mid-Point of AB M X The mid-point is the average of the end points: or

Exercise Find the mid-point, M of the line joining to Solution:

Using Pythagoras’ theorem: This square root is called a surd.

A formula for the length of the line joining A to B Using Pythagoras’ theorem:

e.g. Find the length of the line joining the point to Solution: This can be simplified: 25 is a perfect square, so can be square rooted

Exercise Find the length of the line joining the point to Solution:

SUMMARY The mid-point, M, of the line joining to is the average of the end points. The length of the line joining to is:

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SUMMARY The mid-point, M, of the line joining to is the average of the end points. The length of the line joining to is:

Solution: e.g. Find the mid-point, M of the line joining to

25 is a perfect square, so can be square rooted Solution: e.g. Find the length of the line joining the point to