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Question

The straight lines x+y=0,3x+y4=0 and x+3y4=0 from a triangle which is

A
isosceles
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B
right -angled
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C
obtuse-angled
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D
equilateral
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Solution

The correct options are
B isosceles
C obtuse-angled
Let the given lines be represented by AB,BC and CA, respectively, Then A(2,2),B(2,2) and C(1,1) are the vertices of a triangle ABC.
Also, note that AB=42,AC=10 and BC=10.
This shows that ABC is isosceles; it is clearly not right-angled or equilateral. Since
cosC=BC2+AC2AB22(BC)(AC)=10+103221010<0
ABC is obtuse-angled.

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