Everything Maths Grade 10

Step 2: Assign values to(x 1 ;y 1 )and(x 2 ;y 2 )

Let the mid-point ofEGbeM(x;y)

x 1 = 1 y 1 = 0 x 2 = 8 y 2 = 11

Step 3: Write down the mid-point formula

M(x;y) =

(

x 1 +x 2

2

;

y 1 +y 2

2

)

Step 4: Substitute values calculate the coordinates ofM

M(x;y) =

(

1 + 8

2

;

0 + 11

2

)

=

(

7

2

;

11

2

)

Step 5: Use the coordinates ofMto determineH

Mis also the mid-point ofF Hso we useM

(

7

2

;

11

2

)

andF(0; 3)to solve forH(x;y).

Step 6: Substitute values and solve forxandy

7

2

=

0 +x

2

11

2

=

3 +y

2

7 =x+ 0 11 = 3 +y

x = 7 y = 8

Step 7: Write the final answer

The coordinates ofHare(7; 8).

Exercise 8 – 5:

1.Calculate the coordinates of the mid-point (M) between pointA( 1 ; 3 )and pointB( 3 ; 3 )in the fol-

lowing diagram:

 2  1 1 2 3 4

 4

 3

 2

 1

1

2

3

4

A(1; 3)

B(3;3)

M(x;y)

x

y

Chapter 8. Analytical geometry 313