Answer:
[tex]\sqrt{145}[/tex]
Step-by-step explanation:
The distance formula states that the distance between two points [tex](a,b)[/tex] and [tex](c,d)[/tex] is [tex]\sqrt{(a-c)^2+(b-d)^2}[/tex].
The two points we have are [tex](4,6)[/tex] and [tex](-4,-3)[/tex]. Plugging these numbers into the distance formula, we have
[tex]\sqrt{(4-(-4))^2+(6-(-3))^2[/tex].
Simplifying with order of operations, first using the distributive property, gives
[tex]\sqrt{(4+4)^2+(6+3)^2[/tex].
Squaring and adding gives
[tex]\sqrt{(4+4)^2+(6+3)^2}=\sqrt{8^2+9^2}\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~=\sqrt{64+81}\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~=\boxed{\sqrt{145}},[/tex]
which is the answer in simplest form. This also rounds to about 12.04.
