Question

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

Answer 1

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

$\sqrt{(25 + 144)}$

Now for the addition

$\sqrt{(25+144)}$

25 + 144 = 169

Now take the square root

$\sqrt{169}$ = 13

This segment is 13 units long

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer 2

Answer:

13

Step-by-step explanation:

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

=$\sqrt{5^{2}+12^{2} }$

=13