Determinant Practice Questions Ques8
Question: What is the area of a triangle with vertices at $(1, 0)$, $(6, 0)$, and $(4, 3)$?
Options:
(A) $\frac{11}{2}$ sq. units
(B) $\frac{17}{2}$ sq. units
(C) $\frac{13}{2}$ sq. units
(D) $\frac{15}{2}$ sq. units
Show Answer
Answer: C
Explanation:
Area of triangle $=\frac{1}{2 }\left|\begin{array}{lll}1 & 0 & 1 \\ 6 & 0 & 1 \\ 4 & 3 & 1\end{array}\right|$ Expanding along second column,
$ \begin{aligned} & \Delta=\frac{1}{2}\left[-3\left|\begin{array}{ll} 1 & 1 \\ 6 & 1 \end{array}\right|\right] \\ & =\frac{1}{2}[-3(1-6)] \\ & \Rightarrow \Delta=\frac{15}{2} \text { sq. units } \end{aligned} $
BETA
