X=20
Explanationthe distance between 2 points is given by
[tex]\begin{gathered} for \\ P1(x_1,y_1) \\ P2(x_2y_2) \\ d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \end{gathered}[/tex]
so
Step 1
a)given
[tex]\begin{gathered} P1(12,7) \\ P2(x,-8) \\ d=17 \end{gathered}[/tex]
b) now, replace in the formula and solve for x
[tex]\begin{gathered} d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\ 17=\sqrt{(x-12)^2+(-8-7)^2} \\ 17=\sqrt{(x-12)^2+(-15)^2} \\ raise\text{ both sides to power 2} \\ 17^2=(\sqrt{(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} \\ \sqrt{64}=\sqrt{(x-12)^2} \\ 8=x-12 \\ add\text{ 12 in both sides} \\ 8=x-12 \\ 8+12=x-12+12 \\ 20=x \end{gathered}[/tex]
therefore, the answer is
X=20
I hope this helps you
