Read the foxtrot comic strip. write an explanation, including graphs or diagrams, confirming that running "10 yards out, then 10 yards to the right" puts you in the same place as going "10 2 yards at a 45-degree angle."

You want to drwa a diagram

ok, so 10√2 yards at a 45 degree angle

alrighty

let's use a graphing plane
our starting point is at (0,0), the origin
if we go 10 right and 10 up, we end up at (10,10)
now, if we were to draw a line from our starting point (the origin) to the ending point (10,10), we get a line (duh)
if we measure the angle between the line and the x axis, we get 45 degrees
if we find the distance from (0,0) to (10,10) using the distaance formula, we get 10√2  is the distance from (0,0) to (10,10)

so going 10 out and 10 right is same as 10√2 at 45 degree angle

or you could draw a triangle (see diagram)
legs are 10 and 10, connect them to get a hypotnuse
since the legs are equal lengths, the angles are 45-45-90, we have a 45-45-90 triangle
we can either use the special properies of a 45-45-90 triangle (side lenghs are x:x:x√2) or use pythagorean

so remember if te legs are a,b,,c then a²+b²=c²
a=b=10
10²+10²=c²
100+100=c²
200=c²
sqrt both sides
10√2=c

the lenght is 10√2 at a 45 degree angle