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rectangular cartensian co-ordinates — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSrectangular cartensian co-ordinates1 Mark
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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