Question

How do you find the distance between points (3,-3), (7,2)?

Answer 1

`d=sqrt(41)`

Explanation:

Use the distance formula: `d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)`
If we let `(3,-3)->(color(blue)(x_1),color(red)(y_1))` and `(7,2)->(color(blue)(x_2),color(red)(y_2))` then...

`d=sqrt((color(blue)(7-3))^2+(color(red)(2--3))^2)`

`d=sqrt((color(blue)(4))^2+(color(red)(5))^2)`

`d=sqrt((color(blue)(16))+(color(red)(25))`

`d=sqrt(41)`

Answer 2

The distance between points (3,-3), (7,2) is `d=sqrt41`

That is `approx6.4 units`

Explanation:

Use the distance formula which is derived from the Pythagorean Theorem.

They did it here:
http://www.purplemath.com/modules/distform.htm

`d^2 = (x_2-x_1)^2+(y_2-y_1)^2`

We have points (3,-3), (7,2):

Then: `d^2 = (3-7)^2+(-3-2)^2`

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

See how squaring gets rid of those nasty negatives?

`d^2 = (16)+(25)`

Too bad we cannot take the roots of the two terms without adding.

`d^2 = 41`

`d = sqrt41 approx 6.4`

To check, compare this `right angle triangle 4, 5, 6.4` to a standard `right angle triangle3, 4, 5`, and they appear to be similar.