# Question #5235c

Feb 24, 2016

Our goal is calculating the modulus of the substraction vector, which gives us the distance between both points.

#### Explanation:

We must calculate the modulus of red vector, with coordinates $\left(x , y\right)$. First of all, let us find the value of $x$ and $y$.
Given that the sum of two vectors is another one, with initial point on the initial point of the first one, and terminal point on the terminal point on the second one: vector $\left(4 , 3\right)$ plus $\left(x , y\right)$ equals to $\left(2 , 7\right)$.

$\left(4 , 3\right) + \left(x , y\right) = \left(2 , 7\right) \rightarrow \left(x , y\right) = \left(2 , 7\right) - \left(4 , 3\right) = \left(- 2 , 4\right)$

And now, let us obtain the modulus of this vector, by using the usual generalized Pythagoras theorem :

$\left\mid \left(- 2 , 4\right) \right\mid = \sqrt{{\left(- 2\right)}^{2} + {4}^{2}} = \sqrt{20} = 2 \sqrt{5} = 4.47$