Straight Line And Pair Of Straight Lines Ques 88

  1. 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

Show Answer

Answer:

Correct Answer: 88.(a)

Solution:

Formula:

Distance Formula :

  1. 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.

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