MCQ
The points $( - a,\, - b),\;(0,\,0),\;(a\,,b)$ and $({a^2},ab)$ are
- ✓Collinear
- BVertices of a rectangle
- CVertices of a parallelogram
- DNone of these
✓
Answer
Correct option: A.
Collinear
a
(a) Here area of quadrilateral is equal to area of $\Delta ABD$+area of $\Delta BCD$
$ = \left| {\begin{array}{*{20}{r}}{ - a}&{ - b}&1\\0&0&1\\{{a^2}}&{ab}&1\end{array}\,} \right| + \left| {\begin{array}{*{20}{r}}0&0&1\\a&b&1\\{{a^2}}&{ab}&1\end{array}\,} \right| = 0$
(a) Here area of quadrilateral is equal to area of $\Delta ABD$+area of $\Delta BCD$
$ = \left| {\begin{array}{*{20}{r}}{ - a}&{ - b}&1\\0&0&1\\{{a^2}}&{ab}&1\end{array}\,} \right| + \left| {\begin{array}{*{20}{r}}0&0&1\\a&b&1\\{{a^2}}&{ab}&1\end{array}\,} \right| = 0$
Hence the points are collinear.
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