The area of triangle formed by the lines x-0- y-0 and x-a-y-b-1- a and b are positive- is A- a b-2B- a bC- 2 a bD- a b-3

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Standard XI

Mathematics

Intercept of a Straight Line

The area of t...

Question

The area of triangle formed by the lines x = 0, y = 0 and $\frac{x}{a} + \frac{y}{b} = 1$ , a and b are positive , is

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Solution

The correct option is B
The intersection of these lines are A(0,0), B(a,0), C(0,b). Hence we get a right angled triangle which is right angled at origin.
Length of perpendicular is b and length of base is a.
Area of the right angled triangle is
= $\frac{1}{2} (P e r p e n d i c u l a r) \times (b a s e) = \frac{1}{2} a b$ .

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The area of triangle formed by the lines x = 0, y = 0 and xa+yb=1, a and b are positive , is

The correct option is B The intersection of these lines are A(0,0), B(a,0), C(0,b). Hence we get a right angled triangle which is right angled at origin. Length of perpendicular is b and length of base is a. Area of the right angled triangle is =12(Perpendicular)×(base)=12ab.

The area of triangle formed by the lines x = 0, y = 0 and $\frac{x}{a} + \frac{y}{b} = 1$ , a and b are positive , is