# How do you find the magnitude of YZ given Y(5,4) and Z(0,-3)?

Aug 26, 2016

$Y Z = 8.602$

#### Explanation:

The magnitude between two points $A \left({x}_{1} , {y}_{1}\right)$ and $B \left({x}_{2} , {y}_{2}\right)$ is the distance between A and B and is given by $\sqrt{{\left({x}_{2} - {x}_{1}\right)}^{2} + {\left({y}_{2} - {y}_{1}\right)}^{2}}$.

Hence magnitude of $Y \left(5 , 4\right)$ and $Z \left(0 , - 3\right)$ is

$Y Z = \sqrt{{\left(0 - 5\right)}^{2} + {\left(- 3 - 4\right)}^{2}}$

= $\sqrt{{\left(- 5\right)}^{2} + {\left(- 7\right)}^{2}}$

= $\sqrt{25 + 49}$

= $\sqrt{74} = 8.602$