(-2,1) and (5,-6) solve using the pythagorean theorem
I have tried 
d= the square root of (x-x)^2+(y-y)^2
d= the square root of (-2-5)^2+(1-6)^2
d= the square root of (-7)^2+(-5)^2
d= the square root of 49+25
d= the square root of 74 
i know this is wrong, especially since i'm supposed to solve using the
pythagorean theorem! Please help--thank you!


What they want you to do is to find the distance between the points
(-2,1) and (5,-6) using the Pythagorean theorem:

First, I'll show you how to do it by drawing a graph, and then you
will understand how to use the formula as well as why it works.
Then things will be lots easier for you if you will learn where
the formula comes from:

Here's the graph of the line segment connecting them, in red:


So what you do is draw a horizontal line from (-2,1) to the right
until it is directly above the point (5,-6), like the green line below:



Now you can count the units of the horizontal green line, using the x-axis
as if it were a ruler and see that the green line is 7 units long

Now draw a vertical line from the end of the green line down to the point
(5,-6), like this (in blue):



Now you can count the units of the vertical blue line, using the y-axis
as if it were a ruler and see that the blue line is also 7 units long.

Now you have a right triangle, so you can use the Pythagorean theorem to
find the red line, which is the hypotenuse. So:

green line = a, blue line = b, red line = c

so a = 7 and b = 7

c2 = a2 + b2

c2 = 72 + 72

c2 = 49 + 49

c2 = 98
      __
 c = Ö98
      ____
 c = Ö49·2
      __  _
 c = Ö49·Ö2  
       _
 c = 7Ö2 or about 9.899494937

Or, without drawing the graph, you could find 
the length of the green line by subtracting the
x-coordinates of the two points, like this:

(x2 - x1) = 5 - (-2) = 5 + 2 = 7

Also, without drawing the graph, you could find 
the length of the blue line by subtracting the
y-coordinates of the two points:

(y2 - y1) = -6 - 1 = -7

Then you could use the formula:
     _______________________
d = Ö(x2 - x1)2 + (y2 - y1)2
     _______________________ 
d = Ö(5 - (-2))2 + (-6 - 1)2
     ________________
d = Ö(5 + 2)2 + (-7)2
     _______
d = Ö72 + 72
     _______
d = Ö49 + 49
     __
d = Ö98
     ____
d = Ö49·2
     __  _
d = Ö49·Ö2  
      _
d = 7Ö2 or about 9.899494937

Edwin