Question

A line passes through point (2, 2) find the equation of the line if the length of the line segment intercepted by the coordinate axes is the square root of 5

• A. 2x + y - 2 =0
• B. 2x - y - 2 = 0
• C. 2x - y + 2 = 0
• D. 2x + y + 2 = 0

Answer 1

Answer: (B)

2x - y - 2 = 0

Let A=$(2,2)$ and

B=$(x,y)$

Given,the lenght of the line segment AB is $\sqrt{5}$

$=>\sqrt{(2-x{)}^2+(2-y{)}^2}=\sqrt{5}$

$=>4+x^2-4x+4+y^2-4y=5$

$=>x^2+y^2-4x-4y=-3$

By using trial and error method we take $x=1$,putting the value we get,

$1^2+y^2-4\left(1\right)-4y=-3$

$=>y^2-4y=-0$

$\therefore y=0$

$\therefore$ The coordinates of $B=(1,0)$

We know the equation of the line is $y=mx+c$

Now, the slope (m)=$\frac{y_2-y_1}{x_2-x_1}$

$=>\frac{0-2}{1-2}$

$=2$

Putting the vlaue of $x,y$ and $m$ in the equation formulae we get,

$0=2\left(1\right)+c$

$=>c=-2$

$\therefore$ The equation of the line segment is

$y=2\left(x\right)-2$

$=>2x-y-2=0$