Question

Given (12 ,7)and (X,-8) find all x such that the distance between these two points is 17 separate multiple answers with a comma

Answer 1

X=20

Step-by-step explanation

the distance between 2 points is given by

`\begin{gathered} for \\ P1(x_1,y_1) \\ P2(x_2y_2) \\ d=√((x_2-x_1)^2+(y_2-y_1)^2) \end{gathered}`

so

Step 1

a)given

`\begin{gathered} P1(12,7) \\ P2(x,-8) \\ d=17 \end{gathered}`

b) now, replace in the formula and solve for x

`\begin{gathered} d=√((x_2-x_1)^2+(y_2-y_1)^2) \\ 17=√((x-12)^2+(-8-7)^2) \\ 17=√((x-12)^2+(-15)^2) \\ raise\text{ both sides to power 2} \\ 17^2=(√((x-12)^2+(-15)^2))^2 \\ 289=(x-12)^2+225 \\ subtract\text{ 225 in both sides} \\ 289-225=(x-12)^2+225-225 \\ 64=(x-12)^2 \\ square\text{ root in both sides} \\ √(64)=√((x-12)^2) \\ 8=x-12 \\ add\text{ 12 in both sides} \\ 8=x-12 \\ 8+12=x-12+12 \\ 20=x \end{gathered}`

therefore, the answer is

X=20

I hope this helps you