first we find x of p:
[tex]x = 2 \times ( - 3) - \frac{1}{2} \times 4 + \frac{2}{5} \times 5 \\ = - 6 - 2 + 2 = - 6[/tex]
then we find y of p:
[tex]y = 2 \times 2 - \frac{1}{2} \times ( - 6) - \frac{2}{5} \times ( - 10) \\ = 4 + 3 + 4 = 11[/tex]
so
[tex]p = \binom{ - 6}{11} [/tex]
and
[tex] |p| = \sqrt{ {( - 6)}^{2} + {11}^{2} } \\ = \sqrt{36 + 121} = \sqrt{157} = 12.53[/tex]
