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

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSrectangular cartensian co-ordinates1 Mark
MCQ
The area of triangle formed by the points $(a,b + c),$ $(b,c + a),$ $(c,\,a + b)$ is equal to
  • A
    $abc$
  • B
    ${a^2} + {b^2} + {c^2}$
  • C
    $ab + bc + ca$
  • ✓
    $0$
✓

Answer

Correct option: D.
$0$
d
(d) Area of triangle $ = \frac{1}{2}\left| {\,\begin{array}{*{20}{c}}a&{b + c}&1\\b&{c + a}&1\\c&{a + b}&1\end{array}\,} \right|$
$ = \frac{1}{2}\left| {\,\begin{array}{*{20}{c}}{a + b + c}&{b + c}&1\\{b + c + a}&{c + a}&1\\{c + a + b}&{a + b}&1\end{array}\,} \right|$
$ = \frac{1}{2}(a + b + c)\,\left| {\begin{array}{*{20}{c}}1&{b + c}&1\\1&{c + a}&1\\1&{a + b}&1\end{array}} \right| = 0$.

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