Here given points are A (1, 2) and B (6, 7) which is divided into 5 equal parts by points P, Q, R and S
∴ AP = PQ= QR = RS = SB
The point P divides the line segment AB in the ratio 1:4.
By section formula,
x = \(\frac{mx_2+nx_1}{m+n}\), y = \(\frac{my_2+ny_1}{m+n}\)
For point P,
x = \(\frac{1\times6+4\times1}{1+4}\) , y = \(\frac{1\times7+4\times1}{1+4}\)
x = 2 and y = 3
∴ Coordinate of P is (2 ,3 )
The point Q divides the line segment AB in the ratio of 2:3.
For point Q,
x = \(\frac{2\times6+3\times1}{2+3}\) , y = \(\frac{2\times7+3\times1}{2+3}\)
x = 3 and y = 4
∴ Coordinate of Q is (3 ,4 )
The point R divides the line segment AB in the ratio of 3:2.
For point R,
x = \(\frac{3\times6+2\times1}{3+2}\) , y = \(\frac{3\times7+2\times1}{3+2}\)
x = 4 and y = 5
∴ Coordinate of R is (4 , 5 )
