What is the distance between `(15,-4)` and `(7,5)`?

The formula for calculating the distance between two points is:

`d = sqrt((color(red)(x_2) - color(blue)(x_1))^2 + (color(red)(y_2) - color(blue)(y_1))^2)`

Substituting the values from the points in the problem gives:

`d = sqrt((color(red)(7) - color(blue)(15))^2 + (color(red)(5) - color(blue)(-4))^2)`

`d = sqrt((color(red)(7) - color(blue)(15))^2 + (color(red)(5) + color(blue)(4))^2)`

`d = sqrt((-8)^2 + 9^2)`

`d = sqrt(64 + 81)`

`d = sqrt(145)`

Or

`d= 12.042` rounded to the nearest thousandth.

It might not seem like it, but this question just invooves simple Pythagorus on a graph. Instead of getting the two lengths of the known sides, it has to be worked out by finding the length.

However, this is super easy, just fin the change in `x` and the change in `y`.

To get from 15 `to` 7 we go back by 8, however, we are talking about length, so we take it as `abs(-8) = 8`, and not `-8`. Pur horizontal side has a length of 8.

To get from -4 `to` 5 we go up by 9. This will give us a verticle length of 9.

Now we have a right-angled triangle of lengths 8, 9, and `h`, `h` being the hypotenuse (longest side) of the triangle.

To find the length of `h`, we use `a^2 = b^2 + c^2`, where #a=sqrt(b^2+c^2)

We add our values in to get `h=sqrt(8^2+9^2)=sqrt(64+81)=sqrt(145)=12.0415946~~12.0`