Everything Maths Grade 10

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

Let the coordinates ofCbe(x 1 ;y 1 )and the coordinates ofDbe(x 2 ;y 2 ).

x 1 = 2 y 1 = 4 x 2 =x y 2 =y

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 solve forx 2 andy 2

1 =

2 +x 2

2

3 =

4 +y 2

2

1 2 =2 +x 2  3 2 = 4 +y 2

2 =2 +x 2 6 = 4 +y 2

x 2 = 2 + 2 y 2 = 6  4

x 2 = 4 y 2 = 10

Step 5: Write the final answer
The coordinates of pointDare(4;10).

Worked example 13: Using the mid-point formula

QUESTION

PointsE(1; 0),F(0; 3),G(8; 11)andH(x;y)are points on the Cartesian plane. FindH(x;y)ifEF GHis
a parallelogram.

SOLUTION

Step 1: Draw a sketch

 2 2 4 6 8

 2

2

4

6

8

10

E(1; 0)

F(0; 3)

G(8; 11)

H(x;y)

M

x

y

Method: the diagonals of a parallelogram bisect each other, therefore the mid-point ofEGwill be the same as
the mid-point ofF H. We must first find the mid-point ofEG. We can then use it to determine the coordinates
of pointH.

312 8.4. Mid-point of a line