Two sides of a rhombus are along the lines,
Question:

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

2. $(-3,-9)$

3. $(-3,-8)$

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

Correct Option: , 4

Solution:

Clearly $\left(\frac{1}{3},-\frac{8}{3}\right)$ lies on (1)