Straight Line and Pair of Straight Lines 3 Question 5
6. The straight lines $x+y=0,3 x+y-4=0, x+3 y-4=0$ form a triangle which is
(1983, 1M)
(a) isosceles
(b) equilateral
(c) right angled
(d) None of the above
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Answer:
Correct Answer: 6. (a)
Solution:
- The points of intersection of three lines are $A(1,1), B(2,-2), C(-2,2)$.
Now,
$$ \begin{aligned} & |A B|=\sqrt{1+9}=\sqrt{10} \\ & |B C|=\sqrt{16+16}=4 \sqrt{2} \end{aligned} $$
$$ \text { and } \quad|C A|=\sqrt{9+1}=\sqrt{10} $$
$\therefore$ Triangle is an isosceles.
