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Mathematics

Coordinate-Geometry

Easy

Question

If $a comma x subscript 1 comma x subscript 2$ are in G.P. with common ratio r and $b comma y subscript 1 comma y subscript 2$ are in G.P. with common ratio s where s - r = 2, then the area of the triangle with vertices $left parenthesis a comma b right parenthesis comma open parentheses x subscript 1 comma y subscript 1 close parentheses$ and $open parentheses x subscript 2 comma y subscript 2 close parentheses$ is

$|a b (r^{2} - 1)|$
$a b (r^{2} - s^{2})$
$a b (s^{2} - 1)$
$a b r s$

The correct answer is: $open vertical bar a b open parentheses r squared minus 1 close parentheses close vertical bar$

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