Straight Line and Pair of Straight Lines 3 Question 4
5. The points $0, \frac{8}{3},(1,3)$ and $(82,30)$ are vertices of
(a) an obtuse angled triangle
(b) an acute angled triangle
(c) a right angled triangle
(d) None of the above
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Answer:
Correct Answer: 5. (d)
Solution:
- Since, vertices of a triangle are $(0,8 / 3),(1,3)$ and $(82,30)$
Now, $\quad \frac{1}{2}\left|\begin{array}{ccc}0 & 8 / 3 & 1 \ 1 & 3 & 1 \ 82 & 30 & 1\end{array}\right|$
$$ \begin{aligned} & =\frac{1}{2}-\frac{8}{3}(1-82)+1(30-246) \\ & =\frac{1}{2}[216-216]=0 \end{aligned} $$
$\therefore$ Points are collinear.
