Question

Demonstrate, using your own unique example, how to divide a segment by a given

Answer 1

Answer:Say for example we have segment A with endpoints coordinates of (a,b) and (x,y) and we wish to divide the segment into parts. The ratio of division is assumed to be r. In this case, we identify the first coordinates of the segment next to (a,b) by:

(c,d) = ((x-a)/r + a  , (y-b)/r + b) 

This formula is used including the constant portion of the division of the segment, (x-a)/r. The addition, a, can vary depending on the position of the coordinates to be taken. On the other end, before (x,y), the coordinates should be 

(v,w) = (y - (x-a)/r , z - (y-b)/r )

Hope it is right can i get a crown if this helped please

Answer 2

Let two points in one dimensional line segment be , that is number marked on the number line is A(3) and B(15).

Now, Segment AB is to be divided in the ratio of 1:3.

Distance between AB=

           Position of Point B on the Number Line - Position of Point A on the number line

=15-3

=12

→Position of Point on the number line which is divided in the ratio of 1:3 will be

$=3+\frac{1}{3+1}\times [15-3]\\\\=3+\frac{1}{4}\times 12\\\\=3+3\\\\=6$        

→That is at 3 units away from point 3 , that is at Number 6, marked on the number line.

Now Coming to Two dimensional Coordinate system

Consider two points P(6,0) and Q(0,8) in two dimensional coordinate system which is to be divided in the ratio of 1:4.

→Position of Point on the number line which is divided in the ratio of 1:4 will be

$x=6-\frac{1}{4+1}\times [6]\\\\=6-1.2\\\\=4.8\\\\y=0+\frac{1}{4+1}\times [8]\\\\y=\frac{1}{5}\times 8\\\\=1.6$

Coordinate of the point which is divided in the ratio of 1:3 is equal to=(4.8,1.6)