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 $d = 3\sqrt{2}$.
So, $3\sqrt{2}=\sqrt{(x - 2)^2+(6 - 3)^2}$.

Step2: Square both sides

$(3\sqrt{2})^2=(x - 2)^2+(6 - 3)^2$.
$18=(x - 2)^2+9$.

Step3: Simplify the equation

$(x - 2)^2=18 - 9$.
$(x - 2)^2 = 9$.

Step4: Solve for x

$x-2=\pm3$.
When $x - 2 = 3$, $x=3 + 2=5$.
When $x - 2=-3$, $x=-3 + 2=-1$.

Answer:

B. 5 or -1