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Find the point which trisect (4,0,1),(2,4,0).

Asked by Deebu 28th December 2014, 12:20 AM
Answered by Expert
Answer:
A single point cannot trisect a line.
The point may divide the segment in the ratio 1:3 or 2:3
We need two points to trisect a line segment.
Let the coordinates of A be A(4,0,1) and coordinates of B be (2,4,0)
Let P be the point which divides the line segment in the ratio 1:2
and Q be the point which divides the line segment in the ratio 2:1
Thus, using section formula, the coordinates of P are:
P equals open parentheses fraction numerator 1 cross times 2 plus 2 cross times 4 over denominator 1 plus 2 end fraction comma fraction numerator 1 cross times 4 plus 2 cross times 0 over denominator 1 plus 2 end fraction comma fraction numerator 1 cross times 0 plus 2 cross times 1 over denominator 1 plus 2 end fraction close parentheses rightwards double arrow P equals open parentheses 10 over 3 comma 4 over 3 comma 2 over 3 close parentheses S i m i l a r l y comma Q equals open parentheses fraction numerator 2 cross times 2 plus 1 cross times 4 over denominator 2 plus 1 end fraction comma fraction numerator 2 cross times 4 plus 1 cross times 0 over denominator 2 plus 1 end fraction comma fraction numerator 2 cross times 0 plus 1 cross times 1 over denominator 2 plus 1 end fraction close parentheses rightwards double arrow Q equals open parentheses 8 over 3 comma 8 over 3 comma 1 third close parentheses
Answered by Expert 28th December 2014, 1:59 PM
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