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Question

Show that the line segment joining the points (-5, 8) and (10, -4) is trisected by the co-ordinate axes.


Solution

Let P and Q be the point of trisection of the line segment joining the points A (-5, 8) and B (10, -4).
So, AP = PQ = QB

W e space h a v e space A P colon P B space equals 1 colon 2 C o minus o r d i n a t e space o f space t h e space p o i n t space P space a r e open parentheses fraction numerator 1 cross times 10 plus 2 cross times left parenthesis negative 5 right parenthesis over denominator 1 plus 2 end fraction comma fraction numerator 1 cross times left parenthesis negative 4 right parenthesis plus 2 cross times 8 over denominator 1 plus 2 end fraction close parentheses equals open parentheses fraction numerator 10 minus 10 over denominator 3 end fraction comma 12 over 3 close parentheses equals open parentheses 0 comma 4 close parentheses S o space p o i n t space P space l i e s space o n space t h e space Y minus a x i s 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 10 plus 1 cross times left parenthesis negative 5 right parenthesis over denominator 2 plus 1 end fraction comma fraction numerator 2 cross times left parenthesis negative 4 right parenthesis plus 1 cross times 8 over denominator 2 plus 1 end fraction close parentheses equals open parentheses fraction numerator 20 minus 5 over denominator 3 end fraction comma fraction numerator negative 8 plus 8 over denominator 3 end fraction close parentheses equals open parentheses 5 comma 0 close parentheses

So, point Q lies on the x-axis.
Hence, the line segment joining the given points A and B is trisected by the co-ordinate axes.

Mathematics
Concise Mathematics
Standard X

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