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Question

Find the co-ordinates of the points of tri-section of the line joining the points (-3,0) and (6, 6). 


Solution

Let P and Q be the point of trisection of the line segment joining the points A (-3, 0) and B (6, 6).
So, AP = PQ = QB
W e space h a v e space A P colon P B equals 1 colon 2 C o minus o r d i n a t e space o f space p o i n t space P space a r e open parentheses fraction numerator 1 cross times 6 plus 2 cross times left parenthesis negative 3 right parenthesis over denominator 1 plus 2 end fraction comma fraction numerator 1 cross times 6 plus 2 cross times 0 over denominator 1 plus 2 end fraction close parentheses open parentheses fraction numerator 6 minus 6 over denominator 3 end fraction comma 6 over 3 close parentheses open parentheses 0 comma 2 close parentheses W e space h a v e space A Q colon Q B equals 2 colon 1 C o minus o r d i n a t e s space o f space t h e space p o i n t space Q space a r e open parentheses fraction numerator 2 cross times 6 plus 1 cross times left parenthesis negative 3 right parenthesis over denominator 2 plus 1 end fraction comma fraction numerator 2 cross times 6 plus 1 cross times 0 over denominator 2 plus 1 end fraction close parentheses open parentheses 9 over 3 comma 12 over 3 close parentheses open parentheses 3 comma 4 close parentheses

Mathematics
Concise Mathematics
Standard X

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