Question

Find the distance between the points (2, -5) and (-3, 0)

Answer 1

subtract, square, add, sqrt

Answer 2

what do we get when we subtract one point from the other?

(2,-5)
- (-3,0)
--------
? , ?

Answer 3

-1, -5 ???

Answer 4

close; 2 - - 3 = 5

so lets go with 5, -5 :)

what do we get when we square each of those values?

Answer 5

there are 4 steps in all, we are at #2 :)

Answer 6

so it's 5, -5 over 2, 2

Answer 7

no, lets focus on squaring the parts that we found: 5, -5

would you agree that this squares to 25,25 ?

Answer 8

the formula for distance is generally stated as:\[d=\sqrt{(x-x_o)^2+(y-y_o)^2}\]
i tend to put the wrong parts in the wrong places so I like to step thru it:

subtract
square
add
sqrt

Answer 9

given 2 point: (x,y) and (xo,yo)

step1: subtract

( x, y )
- (xo,yo)
---------
x-xo, y-yo

step2: square
(x-xo)^2 , (y-yo)^2

step3: add
(x-xo)^2 + (y-yo)^2

step 4: sqrt
sqrt((x-xo)^2 + (y-yo)^2)

which is how the formula is developed.