Question

Halle el valor de x de tal forma que la distancia entre los puntos dados sea de 2V5 unidades.

b) (2x – 1,2) y (1 + x,x + 4)

Answer 1

The value of x is
`(+/-)√(6)`

Explanation:

The question in English is

Find the value of x so that the distance between the given points is 2V5 units.

(2x - 1,2) and (1 + x,x + 4)

we know that

the formula to calculate the distance between two points is equal to

`d=\sqrt{(y2-y1)^(2)+(x2-x1)^(2)}`

substitute the values

`d=\sqrt{(x+4-2)^(2)+(1+x-2x+1)^(2)}`

`d=\sqrt{(x+2)^(2)+(-x+2)^(2)}`

`d=√(x^2+4x+4+x^2-4x+4)`

`d=√(2x^2+8)`

Remember that

`d=2√(5)\ units`

substitute

`2√(5)=√(2x^2+8)`

squared both sides

`20=2x^2+8\\\\2x^(2)=12\\\\x^(2)=6\\\\x=(+/-)√(6)`

therefore

The value of x is
`(+/-)√(6)`