Question

2.If the distance between the pointsA(2,-2)andB(-1,x) is equal to 5,then the value of x is​

Answer 1

Answer:

2 , - 6

Step-by-step explanation:

Given

,A = (2 , - 2)

B = (-1 , x)

Distance between the two points = 5 units.

To Find :-

Value of 'x'.

How To Do :-

As they gave the value of distance between the points we need to equate that in formula of distance formula and we will get the value of 'x'.

Formula Required :

-Distance Formula :-

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

Solution :-

A = (2 , - 2)

Let,x₁ = 2 , y₁ = - 2

B = (-1 , x)

Let,x₂ = - 1 , y₂ = x

Substituting in distance formula :-

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

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

$5=\sqrt{9+x^2+2(2)(x)+2^2}$

$5=\sqrt{9+x^2+4x+4}$

$5=\sqrt{x^2+4x+13}$

Squaring on both sides :-

$(5)^2=(\sqrt{x^2+4x+13})^2$

25 = x² + 4x + 13

x² + 4x + 13 - 25 = 0

x² + 4x - 12 = 0

x² + 6x - 2x - 12 = 0

x(x + 6) - 2(x + 6) = 0

(x - 2) (x + 6) = 0

x = 2 , - 6

∴ Value of 'x' can be 2 , - 6.

If x is 2 :-

B = (-1 , x) = (-1 , 2)

If x is - 6 :-

B = (-1 , x) = (-1 , -6)