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, $\quad \frac{1}{2}\begin{vmatrix}0 & 8 / 3 & 1 \\ 1 & 3 & 1 \\ 82 & 30 & 1\end{vmatrix}$
$ \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.
