The difference between the points is ![$\sqrt{53}$](https://tex.z-dn.net/?f=%24%5Csqrt%7B53%7D%24)
Explanation:
The coordinate of point B is ![$(2,7)$](https://tex.z-dn.net/?f=%24%282%2C7%29%24)
The coordinate of point D is ![$(4,14)$](https://tex.z-dn.net/?f=%24%284%2C14%29%24)
The difference between the points can be determined using the formula,
![$d=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}$](https://tex.z-dn.net/?f=%24d%3D%5Csqrt%7B%5Cleft%28x_%7B2%7D-x_%7B1%7D%5Cright%29%5E%7B2%7D%2B%5Cleft%28y_%7B2%7D-y_%7B1%7D%5Cright%29%5E%7B2%7D%7D%24)
Substituting the coordinates
and
, in the formula, we get,
![$d=\sqrt{\left(4-2\right)^{2}+\left(14-7\right)^{2}}$](https://tex.z-dn.net/?f=%24d%3D%5Csqrt%7B%5Cleft%284-2%5Cright%29%5E%7B2%7D%2B%5Cleft%2814-7%5Cright%29%5E%7B2%7D%7D%24)
Subtracting, we get,
![$d=\sqrt{\left(2\right)^{2}+\left(7\right)^{2}}$](https://tex.z-dn.net/?f=%24d%3D%5Csqrt%7B%5Cleft%282%5Cright%29%5E%7B2%7D%2B%5Cleft%287%5Cright%29%5E%7B2%7D%7D%24)
Squaring the terms, we have,
![$d=\sqrt{\left4+\left49}$](https://tex.z-dn.net/?f=%24d%3D%5Csqrt%7B%5Cleft4%2B%5Cleft49%7D%24)
Adding, we get,
![d=$\sqrt{53}$](https://tex.z-dn.net/?f=d%3D%24%5Csqrt%7B53%7D%24)
Hence, the difference between the points is ![$\sqrt{53}$](https://tex.z-dn.net/?f=%24%5Csqrt%7B53%7D%24)