Question

given (10,5) and (x,-10), find all x such that the distance between these two points is 17. separate multiple answers with a comma.

Answer 1

Answer:

x = (2, 18)

Step-by-step explanation:

Given the points (10, 5) and (x, -10)

The distance between these points is:

`\begin{gathered} D=\sqrt[]{(x-10)^2+(-10-5)^2} \\ \\ =\sqrt[]{(x-10)^2+(-15)^2} \\ \\ =\sqrt[]{(x-10)^2+225} \end{gathered}`

The distance is given to be 17, so

`\begin{gathered} \sqrt[]{(x-10)^2+225}=17 \\ \\ (x-10)^2+225=17^2 \\ (x-10)^2=17^2-225 \\ (x-10)^2=289-225 \\ (x-10)^2=64 \\ x-10=\pm\sqrt[]{64}=8 \\ x=\pm8+10 \\ x=8+10=18 \\ OR \\ x=-8+10=2 \end{gathered}`

x = 2 or x = 18