Find the distance between the points (-1,2) and (3,4). Express your answer in the simplest radical form.
We use the distance formula:
$\sqrt{((-1) - 3)^2 + (2 - 4)^2} = \sqrt{(-4)^2 + (-2)^2} = \sqrt{16 + 4} = \sqrt{20} = \boxed{2\sqrt{5}}$.
bro explain the equation
Certainly! The distance formula is used to find the distance between two points in a coordinate plane. It is derived from the Pythagorean theorem.
Let's take two points $(-1,2)$ and $(3,4)$. The distance between these points is given by
$\sqrt{((-1) - 3)^2 + (2 - 4)^2}$.
To simplify this expression, we start by finding the difference between the x-coordinates, which is $-1 - 3 = -4$.
Next, we find the difference between the y-coordinates, which is $2 - 4 = -2$.
We square each of these differences to get $(-4)^2 = 16$ and $(-2)^2 = 4$.
Adding these quantities gives $16 + 4 = 20$.
Finally, we take the square root of this sum to get $\sqrt{20}$.
Since $\sqrt{20}$ cannot be simplified further, the distance between the two points is $\boxed{2\sqrt{5}}$.