[tex]\huge{\boxed{\sqrt{65}}}\ \ \boxed{\text{approx. 8.06225775}}[/tex]
The distance formula is [tex]\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are the points.
Substitute in the values. [tex]\sqrt{(3-(-1))^2 + (-5-2)^2}[/tex]
Simplify the negative subtraction. [tex]\sqrt{(3+1)^2 + (-5-2)^2}[/tex]
Add and subtract. [tex]\sqrt{4^2 + (-7)^2}[/tex]
Solve the exponents. [tex]\sqrt{16 + 49}[/tex]
Add. [tex]\sqrt{65}[/tex]
[tex]65[/tex] has no square factors, so this is as simple as the answer can get. You can use a calculator to find that [tex]\sqrt{65}[/tex] is approximately [tex]8.06225775[/tex].
The formula for distance between two points is:
[tex]\sqrt{(x_{2} -x_{1})^{2} + (y_{2} -y_{1})^{2}}[/tex]
In this case:
[tex]x_{2} =3\\x_{1} =-1\\y_{2} =-5\\y_{1} =2[/tex]
^^^Plug these numbers into the formula for distance like so...
[tex]\sqrt{(3 -(-1))^{2} + (-5-2)^{2}}[/tex]
To solve this you must use the rules of PEMDAS (Parentheses, Exponent, Multiplication, Division, Addition, Subtraction)
First we have parentheses. Remember that when solving you must go from left to right
[tex]\sqrt{(3 -(-1))^{2} + (-5-2)^{2}}[/tex]
3 - (-1) = 4
[tex]\sqrt{(4)^{2} + (-5-2)^{2}}[/tex]
-5 - 2 = -7
[tex]\sqrt{(4)^{2} + (-7)^{2}}[/tex]
Next solve the exponent. Again, you must do this from left to right
[tex]\sqrt{(4)^{2} + (-7)^{2}}[/tex]
4² = 16
[tex]\sqrt{16 + (-7)^{2}}[/tex]
(-7)² = 49
[tex]\sqrt{(16 + 49)}[/tex]
Now for the addition
[tex]\sqrt{(16 + 49)}[/tex]
16 + 49 = 65
√65 <<<This can not be further simplified so this is your exact answer
Your approximate answer would be about 8.06
***Remember that the above answers are in terms of units
Hope this helped!
~Just a girl in love with Shawn Mendes
