Everything Maths Grade 10

To calculate the coordinates of the mid-pointM(x;y)of any line between the pointsA(x 1 ;y 1 )andB(x 2 ;y 2 ),
we use the following formulae:

 1 1 2 3 4 5

 1

1

2

3

4

5

B(x 2 ;y 2 )

A(x 1 ;y 1 )

M(x;y)

x

y

x=

x 1 +x 2

2

y=

y 1 +y 2

2

From this we obtain the mid-point of a line:

Mid-pointM(x;y) =

(

x 1 +x 2

2

;

y 1 +y 2

2

)

VISIT:

This video shows some examples of finding the mid-point of a line.

See video:2GDFatwww.everythingmaths.co.za

Worked example 10: Calculating the mid-point

QUESTION

Calculate the coordinates of the mid-pointF(x;y)of the line between pointE(2; 1)and pointG(2;2).

SOLUTION

Step 1: Draw a sketch

 3  2  1 1 2 3

 3

 2

 1

1

2

G(2;2)

E(2; 1)

F(x;y)

x

y

Chapter 8. Analytical geometry 309