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Two sides of a rhombus are along the lin...

Two sides of a rhombus are along the lines,`x-y+1=0` and `7x-y-5=0` . If its diagonals intersect at `(-1,-2)` , then which one of the following is a vertex of this rhombus ? (1) `(-3,-9)` (2) `(-3,-8)` (3) `(1/3,-8/3)` (4) `(-(10)/3,-7/3)`

A

(-3, -8)

B

`((1)/(3), -(8)/(3))`

C

`((-(10)/(3), -(7)/(3))`

D

(-3, -9)

Text Solution

Verified by Experts

The correct Answer is:
B

On solving equation of AB and AD, vertex A(1, 2)
`because (-1, -2) " is midpoint of " AC, " vertex C is " (-3, -6).`
Line BC is parallel to AD passing through point C, hence its equation is x-y-3 =0
Line DC is parallel to AB passing through ponit C, hence its equation is 7x-y+15=0
Hence other vertices are
`B((1)/(3), -(8)/(3)) " and "D(-(7)/(3), -(4)/(3))`
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