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The line  intersects the coordinates axes at  and  respectively.  line  bisects the area and the perimeter of the triangle  where  is the origin

 

The number of such lines possible is

 

a)

1

b)

2

c)

3

d)

More than 3



Question ID - 55410 | SaraNextGen Top Answer

The line  intersects the coordinates axes at  and  respectively.  line  bisects the area and the perimeter of the triangle  where  is the origin

 

The number of such lines possible is

 

a)

1

b)

2

c)

3

d)

More than 3

1 Answer
127 votes
Answer Key / Explanation : (a) -

(a)

Case I: Let the line  cut  and  at distance  and  from . Then, the area of the triangle with sides  and  is

Also,  (from perimeter bisection). Then  and  are roots of  which has imaginary roots

Case II: If the line  cuts  and  at distance  and  from , then we have  and

Solving, we get  and

Case III: If the line  cuts the sides  and  at distances  and  from , then

 and

  (not possible)

So there is a unique line possible. Let point  be . Using parametric equation of , we have

and 

Hence, slope of  is

127 votes


127