Question

Find the coordinates of points which divide the segment joining A(0,0) and B(4,8) in four congruent segments.

Answer 1

Solve the above question as given below in the attachment.

Answer 2

It can be observed from the figure that points P, Q, R are dividing the line segment in a ratio 1:3, 1:1 , 3:1 respectively.

use formula ,
$\bf{(x,y)=\{\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n}\}}$

P divides AB into 1 : 3 ratio .
so, P = [(1 × 4 + 3 × 0)/(1 + 3), (1 × 8 + 3 × 0)/(1 + 3)]
= ( 4/4 , 8/4) = (1, 2)

Q divides AB into 1 : 1 ratio,
so, Q = [(0 + 4)/(1 + 1) , (0 + 8)/(1 + 1) ]
= (4/2 , 8/2) = (2, 4)

R divides AB into 3 : 1 ratio,
R = [(3 × 4 + 1 × 0)/(3 + 1), (3 × 8 + 1 × 0)/(3 + 1)]
= (12/4 , 24/4) = (3, 6)

hence, P = (1, 2), Q = (2, 4) and R = (3, 6)