find the distance between (0,9)(-40,0) answer in simplest form id ont know where to start

Answer 1

first place is to check your text for some kind of distance formula.

Next, get out some graph paper and plot the two points, then draw a line between them. Call them A and B, respectively.

Now draw a horizontal line from A and a vertical line from B. Where the two lines intersect, call that point C.

Now you have a right triangle, with the right angle at C, and the hypotenuse is AB.

Now recall your Pythagorean Theorem, which says that if the two legs of a right triangle are a and b, and the hypotenuse is c, then

c^2 = a^2+b^2

That is also your distance formula, where
a = x2-x1 = (-40-0)
b = y2-y1 = (0-9)

So, c^2 = 40^2+9^2 = 1609
c = √1609 = 40.11

If you look carefully at the distance formula

d = √(x2-x1)^2 + (y2-y1)^2)

you see that it's really just the Pythagorean Theorem in the context of coordinates, rather than side lengths.