The line intersects the coordinates axes at and respectively. line bisects the area and the perimeter of the triangle where is the origin |
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The number of such lines possible is |
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a) |
1 |
b) |
2 |
c) |
3 |
d) |
More than 3 |
The line intersects the coordinates axes at and respectively. line bisects the area and the perimeter of the triangle where is the origin |
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|
The number of such lines possible is |
|||||||
|
a) |
1 |
b) |
2 |
c) |
3 |
d) |
More than 3 |
(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