In what ratio is the join of (4, 3) and (2, -6) divided by the x-axis ? Also, find the co-ordinates of the point of intersection.

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Solution

Let the point P (x, 0) on x-axis divides the line segment joining A (4, 3) and B (2, -6) in the ratio k: 1.
Using section formula, we have:
$0 equals fraction numerator negative 6 k plus 3 over denominator k plus 1 end fraction 0 equals negative 6 k plus 3 k equals 1 half T h u s space comma t h e space r e q u i r e d space r a t i o n space i s space 1 colon 2 A l s o comma w e space h a v e space colon x equals fraction numerator 2 k plus 4 over denominator k plus 1 end fraction space equals fraction numerator 2 cross times begin display style 1 half end style plus 4 over denominator begin display style 1 half end style plus 1 end fraction space equals 10 over 3 T h u s space comma t h e space r e q u i r e d space c o minus o r d i n a t e s space o f space p o i n t s space o f space i n t e r s e c t i o n space a r e space open parentheses 10 over 3 comma 0. close parentheses$

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In what ratio is the join of (4, 3) and (2, -6) divided by the x-axis ? Also, find the co-ordinates of the point of intersection.

Let the point P (x, 0) on x-axis divides the line segment joining A (4, 3) and B (2, -6) in the ratio k: 1. Using section formula, we have: