Question

Distance between points (-1,2) and (3,-5)

Answer 1

$\huge{\boxed{\sqrt{65}}}\ \ \boxed{\text{approx. 8.06225775}}$

The distance formula is $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$, where $(x_1, y_1)$ and $(x_2, y_2)$ are the points.

Substitute in the values. $\sqrt{(3-(-1))^2 + (-5-2)^2}$

Simplify the negative subtraction. $\sqrt{(3+1)^2 + (-5-2)^2}$

Add and subtract. $\sqrt{4^2 + (-7)^2}$

Solve the exponents. $\sqrt{16 + 49}$

Add. $\sqrt{65}$

$65$ has no square factors, so this is as simple as the answer can get. You can use a calculator to find that $\sqrt{65}$ is approximately $8.06225775$.

Answer 2

The formula for distance between two points is:

$\sqrt{(x_{2} -x_{1})^{2} + (y_{2} -y_{1})^{2}}$

In this case:

$x_{2} =3\\x_{1} =-1\\y_{2} =-5\\y_{1} =2$

^^^Plug these numbers into the formula for distance like so...

$\sqrt{(3 -(-1))^{2} + (-5-2)^{2}}$

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

$\sqrt{(3 -(-1))^{2} + (-5-2)^{2}}$

3 - (-1) = 4

$\sqrt{(4)^{2} + (-5-2)^{2}}$

-5 - 2 = -7

$\sqrt{(4)^{2} + (-7)^{2}}$

Next solve the exponent. Again, you must do this from left to right

$\sqrt{(4)^{2} + (-7)^{2}}$

4² = 16

$\sqrt{16 + (-7)^{2}}$

(-7)² = 49

$\sqrt{(16 + 49)}$

Now for the addition

$\sqrt{(16 + 49)}$

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