Go To Your Study Dashboard

Get Answers to all your Questions

header-bg

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)

best_answer

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

Posted by

divya.saini

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Main 2024 Topper: Farmer’s son Gajare Nilkrishna says ‘keep questioning until you understand’

anam-khan

NIT Puducherry Cut-off 2024: Computer Science and Engineering had highest closing rank last year

anam-khan

JEE Mains: Farmer's son from remote Maharashtra village aces exam

Latest Question