Everything Maths Grade 10

From the sketch, we can estimate thatFwill lie on they-axis, with a negativey-coordinate.

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

x 1 = 2 y 1 = 2 x 1 = 2 y 2 = 1

Step 3: Write down the mid-point formula

F(x;y) =

(

x 1 +x 2

2

;

y 1 +y 2

2

)

Step 4: Substitute values into the mid-point formula

x=

x 1 +x 2

2

=

2 + 2

2

= 0

y=

y 1 +y 2

2

=

2 + 1

2

=

1

2

Step 5: Write the answer

The mid-point is atF

(

0;^12

)

.

Looking at the sketch we see that this is what we expect for the coordinates ofF.

Worked example 11: Calculating the mid-point

QUESTION

Find the mid-point of lineAB, givenA(6; 2)andB(5;1).

SOLUTION

Step 1: Draw a sketch

 6  2 2 6

 2

 1

1

2

3

B(5;1)

A(6; 2)

M(x;y)

x

y

310 8.4. Mid-point of a line