Question

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

Answer 1

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

`√((16 + 49))`

Now for the addition

`√((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

Answer 2

`\huge{\boxed{√(65)}}\ \ \boxed{\text{approx. 8.06225775}}`

The distance formula is
`√((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.
`√((3-(-1))^2 + (-5-2)^2)`

Simplify the negative subtraction.
`√((3+1)^2 + (-5-2)^2)`

Add and subtract.
`√(4^2 + (-7)^2)`

Solve the exponents.
`√(16 + 49)`

Add.
`√(65)`

`65` has no square factors, so this is as simple as the answer can get. You can use a calculator to find that
`√(65)` is approximately
`8.06225775`.