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 ?

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B

Point of intersection of sides

x – y + 1 = 0

and 7x – y – 5 = 0

$∴ x = 1, y = 2$

Slope of AM $= \frac{4}{2} = 2$

$∴ E q u a t i o n o f B D : y + 2 = - \frac{1}{2} (x + 1)$

$\Rightarrow x + 2 y + 5 = 0$

Solving x + 2y + 5 = 0 and 7x – y – 5 = 0

$x = \frac{1}{3}, y = - \frac{8}{3} \Rightarrow (\frac{1}{3}, - \frac{8}{3})$

Suggest Corrections

Similar questions

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?

Q. Two sides of a rhombus are along the lines

x - y + 1 = 0

and

7 x - y - 5 = 0

.
If its diagonals at

(- 1, - 2)

, then which one of the following is a vertex of this rhombus?

Join BYJU'S Learning Program

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 ?

The correct option is B Point of intersection of sides x – y + 1 = 0 and 7x – y – 5 = 0 ∴x=1,y=2 Slope of AM =42=2 ∴ Equation of BD :y+2=−12(x+1) ⇒x+2y+5=0 Solving x + 2y + 5 = 0 and 7x – y – 5 = 0 x=13,y=−83⇒(13,−83)