Question

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

• A. $(-3,-8)$
• B. $(\frac{1}{3},-\frac{8}{3})$
• C. $(\frac{10}{3},-\frac{7}{3})$
• D. $(-3,-9)$

Answer 1

The correct option is A $(-3,-8)$

The lines, $x-y=0$ and $7x-y-5=0$ are adjacent line of rhombus

Hence they intersects at (solving above line we get ) $(x,y)=(1,2)$

$C$ is point of vertex and diagonal is given $(-1,-2)$

Using mid point theorem we have,

$-1=\frac{x+1}{2},x=-3$

$-2=\frac{y+2}{2},y=-6$

Now using the given lines and coordinates we have

Vertex D as $(-3,-8)$