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)
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 | SaraNextGen Top Answer
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)
|
Sides of a rhombus are parallel to the lines |
|||||||
|
a) |
(8/5, 16/5) |
b) |
(7/15, 14/15) |
c) |
(6/5, 12/5) |
d) |
(4/15, 8/15) |
(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)