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