The point which divides externally the line joining the points (a… - Vidyadip

MCQ

The point which divides externally the line joining the points $(a + b,\,a - b)$ and $(a - b,a + b)$ in the ratio $a:b$, is

✓
$\left( {\frac{{{a^2} - 2ab - {b^2}}}{{a - b}},\frac{{{a^2} + {b^2}}}{{a - b}}} \right)$
B
$\left( {\frac{{{a^2} - 2ab - {b^2}}}{{a - b}},\frac{{{a^2} - {b^2}}}{{a - b}}} \right)$
C
$\left( {\frac{{{a^2} - 2ab + {b^2}}}{{a - b}},\frac{{{a^2} + {b^2}}}{{a - b}}} \right)$
D
None of these

✓

Answer

Correct option: A.

$\left( {\frac{{{a^2} - 2ab - {b^2}}}{{a - b}},\frac{{{a^2} + {b^2}}}{{a - b}}} \right)$

a
(a) Here $x = \frac{{a\,(a - b) - b\,(a + b)}}{{a - b}} = \frac{{{a^2} - 2ab - {b^2}}}{{a - b}}$

$y = \frac{{a\,(a + b) - b\,(a - b)}}{{a - b}} = \frac{{{a^2} + {b^2}}}{{a - b}}$.

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