Question

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

Answer 1

Answer:

Hey

Step-by-step explanation:

Value of X = (6) or (-2)

2 answers are possible

substitute and check which is possible in this case

Hope it helps

Answer 2

Answer:

$\huge\boxed{x=-6\ \vee\ x=2}$

Step-by-step explanation:

The formula of a distance between two points

$A(x_A,\ y_A);\ B(x_B,\ y_B)\\\\d_{AB}=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}$

We have

$P(2,\ 2),\ Q(5,\ x),\ d_{PQ}=5$

substitute

$\sqrt{(5-2)^2+(x-2)^2}=5\\\\\sqrt{3^2+(x-2)^2}=5\\\\\sqrt{9+(x-2)^2}=5\qquad|\text{square both sides}\\\\\left(\sqrt{9+(x-2)^2}\right)^2=5^2\\\\9+(x-2)^2=25\qquad\text{subtract 9 from both sides}\\\\(x-2)^2=16\to x-2=\pm\sqrt{16}\\\\x-2=\pm4\qquad|\text{add 2 to both sides}\\\\x=-4-2\ \vee\ x=4-2\\\\\boxed{x=-6\ \vee\ x=2}$