Question

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

Answer 1

Answer:

The value of x is $(+/-)\sqrt{6}$

Step-by-step 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

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

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

$d=\sqrt{x^2+4x+4+x^2-4x+4}$

$d=\sqrt{2x^2+8}$

Remember that

$d=2\sqrt{5}\ units$

substitute

$2\sqrt{5}=\sqrt{2x^2+8}$

squared both sides

$20=2x^2+8\\\\2x^{2}=12\\\\x^{2}=6\\\\x=(+/-)\sqrt{6}$

therefore

The value of x is $(+/-)\sqrt{6}$