Question

If the distance between point P (2,2) and Q(5,X) is 5 then the value of X is

Answer 1

p (2,2) and Q(5,3) X(5,3)

Answer 2

The value of X are 6,-2.

Step-by-step explanation:

Given : If the distance between point P (2,2) and Q(5,X) is 5.

To find : The value of X ?

Solution :

The distance between two point is given by,

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

Points are $P(x_1,y_1)= (2,2)$ and $Q(x_2,y_2)= (5,X)$

The distance is d=5.

Substitute the values,

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

$5=\sqrt{(3)^2+X^2+4-4X}$

Squaring both side,

$25=9+X^2+4-4X$

$X^2-4X-12=0$

Apply middle term split,

$X^2-6X+2X-12=0$

$X(X-6)+2(X-6)=0$

$(X-6)(X+2)=0$

$X=6,-2$

Therefore, the value of X are 6,-2.

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