Question

given (18, 6) and (x, - 3), find all x such that the distance between these two points is 15. separate multiple answers with a comma.

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, $(x_1,y_1)=(18,6)$ and $(x_2,y_2)=(x, - 3)$ and $d = 15$. So, $15=\sqrt{(x - 18)^2+(-3 - 6)^2}$.

Step2: Square both sides

Squaring both sides to get rid of the square - root: $15^2=(x - 18)^2+(-9)^2$. So, $225=(x - 18)^2 + 81$.

Step3: Isolate the squared term

Subtract 81 from both sides: $(x - 18)^2=225 - 81$. So, $(x - 18)^2 = 144$.

Step4: Take square root of both sides

$x-18=\pm\sqrt{144}=\pm12$.

Step5: Solve for x

Case 1: When $x - 18=12$, then $x=12 + 18=30$. Case 2: When $x - 18=-12$, then $x=-12 + 18 = 6$.

Answer:

$6,30$