Question

the distance between the point (2, 3) and (x, 6) is 3√2. use the distance formula to find the possible values of x. a 4 or - 2 b 5 or - 1 c 9 or 3 d 11 or 8

Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $(x_1,y_1)=(2,3)$ and $(x_2,y_2)=(x,6)$ and $d = 3\sqrt{2}$.

Step2: Substitute values into formula

$3\sqrt{2}=\sqrt{(x - 2)^2+(6 - 3)^2}$. Squaring both sides to get rid of the square - root, we have $(3\sqrt{2})^2=(x - 2)^2+3^2$.

Step3: Simplify the equation

$18=(x - 2)^2 + 9$. Then, $(x - 2)^2=18 - 9=9$.

Step4: Solve for x

Taking the square root of both sides, $x - 2=\pm3$. When $x - 2 = 3$, $x=5$; when $x - 2=-3$, $x=-1$.

Answer:

B. 5 or - 1