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Maths-

General

Easy

Question

The straight lines x + y = 0, 3x + y - 4 = 0 and x + 3y -4 = 0 form a triangle which is

isosceles
right angled
obtuse angled
equilateral

hint Hint:

The correct answer is: obtuse angled

we are given three straight lines and asked what form a triangle is formed
x+y=0 ..... (i) 3x+y−4=0 ..... (ii) x+3y−4=0 ....... (iii)
Solving lines (i) and (ii), we get
−x=−3x+4⟹x=2⟹y=−2
∴(i) and (ii) intersect at A=(2,−2)
Solving lines (ii) and (iii), we get−3x+4=34−x⟹−9x+12=4−x⟹x=1⟹y=1
∴(ii) and (iii) intersect at B=(1,1)
Solving lines (i) and (iii), we get−x=34−x⟹−3x=4−x⟹x=−2⟹y=2∴(i) and (iii) intersect at C=(−2,2)
So, AB,BC,AC form a triangle ABCNow, AB=(1−2)2+(1+2)2=10BC=(−2−1)2+(2−1)2=10AC=(−2−2)2+(2+2)2=32∴AB=BCAs two sides of a triangle are equal then the triangle formed by A,B,C is isosceles triangle.

therefore it forms an isosceles triangle

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