Respuesta :
Answer:
[tex]x=5 \ and \ x=-7[/tex]
Step-by-step explanation:
We apply distance formula to find length of AB.
Distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]A(-1,10)\textrm{ } B(x,2)\\\textrm{Length of AB=} \sqrt{(x-(-1))^2+(2-10)^2}=\sqrt{(x+1)^2+(-8)^2}=\sqrt{(x+1)^2+64}\\\textrm{Length of AB=}10\\\sqrt{(x+1)^2+64}=10\\ \textrm{Squaring both sides}\\\\(\sqrt{(x+1)^2+64 })^2=10^2\\ (x+1)^2+64=100\\\textrm{Subtracting both sides by 64}\\(x+1)^2+64-64=100-64\\(x+1)^2=36\\\textrm{Taking square root both [tex]sides}\\\sqrt{(x+1)^2}=\sqrt{36} \\ x+1=\pm6\\\textrm{Subtracting both sides by 1}\\x+1-1=\pm6-1[/tex]
[tex]x=6-1=5\\x=5\\\textrm{and }\\x=-6-1=-7\\x=-7[/tex]
[tex]\therefore\textrm{ } x=5\ and \x=-7[/tex]
The value of x are x=-7 and x=5
A(-1,10) and B(x,2) also AB = 10.
We have to find the the value of x
What is the distance formula?
[tex]AB=\sqrt{(x_{1}-x_{2 })^{2}+(y_{1}-y_{2}) ^{2} }[/tex]
[tex](x_{1},y_{1})=(-1,10) \\(x_{2},y_{2})=(x,2)[/tex]
[tex]AB=\sqrt{(x-(-1 ))^{2}+(10-{2}) ^{2} }[/tex]
[tex]10=\sqrt{(x+1 ))^{2}+(8) ^{2} }[/tex]
[tex]10=\sqrt{(x+1 ))^{2}+64 }[/tex]
squaring on both side we get
[tex]100=(x+1 ))^{2}+64[/tex]
Subtracting 64 from both side
[tex]100-64=(x+1 )^{2}+64-64[/tex]
[tex](x+1 )^{2}=36[/tex]
Taking square root on both side we get
x+1=±6
x+1=6
x=6-1=5
or x+1=±-6
x=-6-1
x=-7
The value of x are x=-7 and x=5
To learn more about the distance visit:
https://brainly.com/question/1872885
