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 ?

  • Option 1)

    (−3, −9)

     

  • Option 2)

    (−3, −8)

     

  • Option 3)

    \left ( \frac{1}{3} ,-\frac{8}{3}\right )

  • Option 4)

    \left (- \frac{10}{3},-\frac{7}{3} \right )

 

Answers (2)

As we learnt in 

Slope – point from of a straight line -

y-y_{1}=m(x-x_{1})

- wherein

m\rightarrow slope

\left ( x_{1},y_{1} \right )\rightarrow point through which line passes

 Point of intersection of AB and AD is A\left ( 1,2 \right )

Let C be \left ( x_{1}, y_{1} \right )

\frac{x_{1}+1}{2} = -1 

and  \frac{y_{1}+2}{2} = -2

x=-3\:;y=-6

C\left ( -3,-6 \right )

Slope of     AC = \frac{2+2}{1+1}=2

Hence, slope of BD= \frac{-1}{2}

equation of BD \Rightarrow \frac{y+2}{x+1} =\frac{-1}{2}

2y+4=-x-1

BD: x+2y+5=0

Point \left ( \frac{1}{3},- \frac{8}{3} \right ) Statistics this line BD


Option 1)

(−3, −9)

 

Incorrect
 

Option 2)

(−3, −8)

 

Incorrect
 

Option 3)

\left ( \frac{1}{3} ,-\frac{8}{3}\right )

Correct
 

Option 4)

\left (- \frac{10}{3},-\frac{7}{3} \right )

Incorrect
 

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