Let's take two points, $A(x_A,y_A)$ and $B(x_B,y_B)$ in the plane.

The length of the blue line is given by $x_B-x_A$, and the length of the red line is given by $y_B-y_A$.

Therefore, the distance between the points can be found using Pythagoras' Theorem:

Let's practise using this formula and applying it to some problems.

1. Use the distance formula to find the exact value of the distance between:

   $$(-1,5)\text{and}(8,-2)$$

2. The distance between the point $(k,3)$ and $(2,5)$ is equal to $7.$

   Find the possible values of $k.$