Question

If the distance between the points A(2,-2) and B(-1, x) is equal to 5, then the value of is: 2 -2 1 -1​

Answer 1

Topic :-

Straight Line

Given :-

The distance between the points A (2, -2) and B (-1, x) is equal to 5.

To Find :-

Value of 'x'.

Concept Used :-

We will be using Distance Formula to calculate the distance between given two points and then equate it with 5.

Distance Formula

$\sf{Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}}$

Solution :-

Considering,

$\sf{A\:(2,-2)\equiv (x_1,y_1)}$

$\sf{B\:(-1,x)\equiv (x_2,y_2)}$

So, we can say that,

$\sf{x_1=2}$

$\sf{y_1=-2}$

$\sf{x_2=-1}$

$\sf{y_2=x}$

It is given that,

Distance = 5

Applying Formula,

$\sf{5=\sqrt{(-1-2)^2+(x-(-2))^2}}$

$\sf{5=\sqrt{(-3)^2+(x-(-2))^2}}$

$\sf{5=\sqrt{(-3)^2+(x+2)^2}}$

Squaring both sides,

$\sf{(5)^2=\left(\sqrt{(-3)^2+(x+2)^2}\right)^2}$

$\sf{25=(-3)^2+(x+2)^2}$

$\sf{25=9+(x+2)^2}$

$\sf{(x+2)^2=25-9}$

$\sf{(x+2)^2=16}$

$\sf{(x+2)^2=4^2}$

Taking root both sides,

$\sf{\sqrt{(x+2)^2}=\sqrt{4^2}}$

$\sf{x+2=\pm 4}$

$\sf{x=-2\pm 4}$

Taking positive sign,

$\sf{x=-2+ 4}$

$\sf{x=2}$

Taking negative sign,

$\sf{x=-2- 4}$

$\sf{x=-6}$

Answer :-

So, the possible value of x are 2 and -6.

Among given options, 2 is correct answer.