Final Cover - For Printing

10. Area of a quadrilateral
    Let A(x 1 ,y 1 ), B(x 2 ,y 2 ), C(x 3 ,y 3 ), D(x 4 ,y 4 ) be the vertices of the quadrilateral ABCD. Then
    the area of the quadrilateral will be equal to the two triangles which are obtained
    upon drawing a diagonal AC for the quadrilateral. Then,

Area of the quadrilateral ABCD = Area of triangle ADC + Area of triangle ACB

The formula used for triangle be applied to find out the area.

11. Condition for collinearity
    Three or more points are said to be collinear if they lie on the same straight line. The
    condition for the three points (x 1 ,y 1 ), (x 2 ,y 2 ),(x 3 ,y 3 ) to be collinear is the area of the
    triangle formed by the three points should be equal to zero.

That is, x 1 (y 2 -y 3 ) + x 2 (y 3 -y 2 ) + x 3 (y 1 -y 2 ) = 0

Alternate method:

Let A(x 1 ,y 1 ),B(x 2 ,y 2 ) and C(x 3 ,y 3 ) be the three given points. To check whether the

given points are collinear, it is enough to show that,

(^1122) x 22 x^33
y -y
x x
y y
− = −

−

At this stage, the child is familiar with the idea of collinear already, and before, the

above example may be easy to understand.

12. Median
    Median is the line passing through the midpoint of a side to the opposite vertex. Note
    that three medians can be drawn to a triangle and all the three medians pass through
    the same point.

B (x, 2 y) 2

D (x, 4 y) 4 C (x, 3 y) 3

A (x, 11 y)