Find the distance between the points (2, -3) and (5, -4).

Question

whpalmer4 · Answer

The distance between two points $(x_1,y_1),(x_2,y_2)$ is given by the formula
$$d = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$$Plug in your points and find the result.  Notice that if the two points share either their x value or their y value, the formula reduces to the difference between the other values.

whpalmer4 · Answer

It doesn't matter which point you choose as $(x_1,y_1)$...

anonymous · Answer

d=(2-5)^2+(-3)-(-4)^2

whpalmer4 · Answer

Close, 
$$d = \sqrt{(2-5)^2+(-3-(-4))^2}$$What does that equal?

anonymous · Answer

d=-23+169?

whpalmer4 · Answer

Mmm...no :-)

$$d = \sqrt{(2-5)^2 + (-3-(-4))^2}$$What is $(2-5)^2$?

anonymous · Answer

-9?

whpalmer4 · Answer

2-5= -3
-3*-3 = ?

anonymous · Answer

9?

whpalmer4 · Answer

Right!  
Now what is -3 - (-4)?

anonymous · Answer

1?

whpalmer4 · Answer

Correct again!  So what is the square root of 9+1?  That's our distance...

whpalmer4 · Answer

You can't factor out any squares from 10, and it isn't a rational number, so you're left writing $$d = \sqrt{10}$$unless you want to break out your calculator and write down a few digits as an approximation.