Everything Maths Grade 10

From the sketch, we can estimate thatMwill lie in quadrant I, with positivex- andy-coordinates.

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

Let the mid-point beM(x;y)
x 1 = 6 y 1 = 2 x 2 = 5 y 2 = 1

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 and simplify

M(x;y) =

(

6 5

2

;

2 1

2

)

=

(

1

2

;

1

2

)

Step 5: Write the final answer

M

( 1

2 ;

1

2

)

is the mid-point of lineAB.

We expectedMto have a positivex- andy-coordinate and this is indeed what we have found by calculation.

Worked example 12: Using the mid-point formula

QUESTION

The line joiningC(2; 4)andD(x;y)has the mid-pointM(1;3). Find pointD.

SOLUTION

Step 1: Draw a sketch

 4  2 2 4 6

 10

 8

 6

 4

 2

2

4

C(2; 4)

D(x;y)

M(1;3)

x

y

From the sketch, we can estimate thatDwill lie in Quadrant IV, with a positivex- and negativey-coordinate.

Chapter 8. Analytical geometry 311