The point ( - 4, 5) is the vertex of a square and one of its diagonals is 7 x -y + 8 = 0. The equation of the other diagonal is

Question

The point ( - 4, 5) is the vertex of a square and one of its diagonals is 7 x -y + 8 = 0. The equation of the other diagonal is (A) 7 x -y + 23 = 0 (B) 7y + x = 30 (C) 7y + x = 31 (D) x - 7y = 30

Tardigrade Admin · Accepted Answer

As we know that diagonals of a square are perpendicular to each other

Let the equation of other diagonal is

x + 7 y = k

Also, passes through

(- 4, 5)

∴ - 4 + 35 = k

\Rightarrow k = 31

∴

Required equation is

x + 7 y - 31 = 0

Q. The point $(- 4, 5)$ is the vertex of a square and one of its diagonals is $7 x - y + 8 = 0$ . The equation of the other diagonal is

$7 x - y + 23 = 0$

$7 y + x = 30$

$7 y + x = 31$

$x - 7 y = 30$

As we know that diagonals of a square are perpendicular to each other

Let the equation of other diagonal is

$x + 7 y = k$

Also, passes through $(- 4, 5)$

$∴ - 4 + 35 = k$

$\Rightarrow k = 31$

$∴$ Required equation is $x + 7 y - 31 = 0$

Q. The point (−4,5) is the vertex of a square and one of its diagonals is 7x−y+8=0. The equation of the other diagonal is

7x−y+23=0

7y+x=30

7y+x=31

x−7y=30