Question

How many units long is a segment whose endpoints are (1,2) and (-4,-10)?

Answer 1

13

Explanation:

`\sqrt{|1-(-4)|^(2)+|2-(-10)|^(2)`

=
`\sqrt{5^(2)+12^(2) }`

=13

Answer 2

This question is essentially asking to find the distance between these two points:

The formula for distance between two points is:

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

In this case:

`x_(2) =-4\\x_(1) =1\\y_(2) =-10\\y_(1) =2`

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

`\sqrt{(-4-1)^(2) + (-10-2)^(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{(-4-1)^(2) + (-10-2)^(2)}`

-4 - 1 = -5

`\sqrt{(-5)^(2) + (-10-2)^(2)}`

-10 - 2 = -12

`\sqrt{(-5)^(2) + (-12)^(2)}`

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

`\sqrt{(-5)^(2) + (-12)^(2)}`

(-5)² = 25

`\sqrt{25 + (-12)^(2)}`

(-12)² = 144

`√((25 + 144))`

Now for the addition

`√((25+144))`

25 + 144 = 169

Now take the square root

`√(169)` = 13

This segment is 13 units long

Hope this helped!

~Just a girl in love with Shawn Mendes