If the points (a,b), ,(a',b')and (a - a',b - b')are collinear, th… - Vidyadip

MCQ

If the points $(a,b),\,(a',b')$and $(a - a',b - b')$are collinear, then

✓
$ab' = a'b$
B
$ab = a'b'$
C
$aa' = bb'$
D
${a^2} + {b^2} = 1$

✓

Answer

Correct option: A.

$ab' = a'b$

a
(a) $\frac{{a - a' - a'}}{{a' - a}} = \frac{{b - b' - b'}}{{b' - b}}$

$ \Rightarrow \,\,\,\frac{{a - 2a'}}{{a' - a}} = \frac{{b - 2b'}}{{b' - b}}$

$ \Rightarrow \,\,\frac{a}{{a'}} = \frac{b}{{b'}}\,\,$

$\Rightarrow \,\,ab' = a'b.$

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