Question

If the distance between point p (2,2) and q(5,x) is 5 then the value of x is site:brainly.In

Answer 1

Using Distance formula;

${distance}^{2} = {(x2 - x1)}^{2} + {(y2 - y1)}^{2} \\ {5}^{2} = {(5 - 2)}^{2} + {(x - 2)}^{2} \\ 25 = {3}^{2} + {(x - 2)}^{2} \\ 25 = 9 + {(x - 2)}^{2} \\ {(x - 2)}^{2} = 16 \\ x - 2 = ±4 \\ x = 6,- 2$

Answer 2

Answer:

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}d=

(x

2

−x

1

)

2

+(y

2

−y

1

)

2

Points are P(x_1,y_1)= (2,2)P(x

1

,y

1

)=(2,2) and Q(x_2,y_2)= (5,X)Q(x

2

,y

2

)=(5,X)

The distance is d=5.

Substitute the values,

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

(5−2)

2

+(X−2)

2

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

(3)

2

+X

2

+4−4X

Squaring both side,

25=9+X^2+4-4X25=9+X

2

+4−4X

X^2-4X-12=0X

2

−4X−12=0

Apply middle term split,

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

2

−6X+2X−12=0

X(X-6)+2(X-6)=0X(X−6)+2(X−6)=0

(X-6)(X+2)=0(X−6)(X+2)=0

X=6,-2X=6,−2

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

#Learn more

If the distance between the points (4,p)and (1,0) is 5 ,then find the value of p

https://brainly.in/question/1889874