# Sides of a rhombus are parallel to the lines  and . It is given that diagonals of the rhombus intersect at (1, 3) and one vertex, '' of the rhombus lies on the line . Then the coordinates of the vertex  are a) (8/5, 16/5) b) (7/15, 14/15) c) (6/5, 12/5) d) (4/15, 8/15)

## Question ID - 53809 :- Sides of a rhombus are parallel to the lines  and . It is given that diagonals of the rhombus intersect at (1, 3) and one vertex, '' of the rhombus lies on the line . Then the coordinates of the vertex  are a) (8/5, 16/5) b) (7/15, 14/15) c) (6/5, 12/5) d) (4/15, 8/15)

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(a,c)

It is clear that diagonals of the rhombus will be parallel to the bisectors of the given lines and will pass through (1, 3). Equations of bisectors of the given lines are

or

Therefore, the equations of diagonals are  and . Thus the required vertex will be the point where these lines meet the line . Solving these lines we get possible coordinates as (8/5, 16/5) and (6/5, 12/5)

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 In a  and point '' lies on the line  where  integer and area of the triangle is  such that  where  denotes the greatest integer function. Then all possible coordinates of a) b) c) (2, 7) d) (3, 9)