Answer:
[tex]2\sqrt{5}[/tex]
Step-by-step explanation:
You can use the Pythagorean Theorem, which is [tex]a^{2}+ b^{2}= c^{2}[/tex]. So the the distance from -9 to -5 is 4 and the distance from 8 to 6 is 2.
So [tex]4^{2} +2^{2} =c^{2}[/tex]. Which equals [tex]20=c^{2}[/tex].
Then you square root [tex]c^{2}[/tex] to make it c, then you do that to the other side. So you have [tex]\sqrt{20}=c[/tex].
Which equals [tex]2\sqrt{5}[/tex].
Or you can use the Distance Formula, which is [tex]\sqrt{(x_{2}-x_{1})^{2} +(y_{2}-y_{1})^{2} }[/tex].
The [tex]x_{1}[/tex] is -5 and the [tex]x_{2}[/tex] is -9. The [tex]y_{1}[/tex] is 6 and the [tex]y_{2}[/tex] is 8. When you plug that in you get [tex]\sqrt{(-9--5)^{2} +(8-6))^{2} }[/tex]. When you simplify that you get [tex]\sqrt{20}[/tex].
Which equals [tex]2\sqrt{5}[/tex].
