Question

What is the distance between `(4, 2)` and # (-5, -2) #?

Answer 1

The distance is approximately 9.84.

Explanation:

If you have two points with coordinates `(x_1, y_1)` and `(x_2, y_2)` the distance is given by the Pitagora's theorem as:

`d=sqrt((x_1-x_2)^2+(y_1-y_2)^2)`.
For you this mean
`d=sqrt((4+5)^2+(2+2)^2)=sqrt(9^2+4^2)=sqrt(81+16)=sqrt(97)\approx 9.84`.

Be careful when you apply this formula that you have to use the correct signs. For example I have that the `x` coordinate of the second point is `x_2=-5`. In the formula I have `x_1-x_2` that is `x_1 - (-5)` and the double minus results in a +. This is why you see it with a plus sign.