Question

(1, 2) is vertex of a square whose one diagonal is along the x – axis. The equations of sides passing through the given vertex are

Answer 1

Solution:

(1,2) is vertex of a square whose one diagonal is along x axis.

Equation of x axis is given by , y=0.

Line perpendicular to y=0, is given by→ x+k=0

Since Diagonals of square bisect each other at Right angles.

The Diagonal → x+ k =0 , passes through (1,2).

→ 1 + k =0

→ k= -1

Equation of other diagonal which passes through point (1,2) is → x -1 =0

Equation of line AB passing through (1,2) and making an angle of 45° with x axis is :

$\frac{y-2}{x-1} =tan 45°$

→ y - 2 = 1 × (x-1)

→ y - 2 = x -1

→ x - y + 2-1=0

→ x - y +1 =0

→ Equation of line BC passing through (1,2) and making an angle of 135° with x axis is:

→$\frac{y-2}{x-1} =tan 135°$

→y-2 = -1 (x-1)

→ y - 2 = -x +1

→ x + y=2+1

→ x+ y-3=0

The three lines which passes through (1,2) are

1. x-1=0

2. x -y +1=0

3. x+y-3=0