Question

determine m, sabendo que o ponto P(3,m) dista 10 unidades do ponto A(-3,6)

Answer 1

$Ola' \\ \\ \underbrace{d_{PA}}_{10}= \sqrt{(-3-3)\²+(6-m)\²} \\ \\ 10= \sqrt{(-6)\²+(6-m)\²} \\ \\ 10\²=( \not\sqrt{36+36-12m+m\²}) ^{\not2} \\ \\ 100=72-12m+m\² \\ \\ m\²-12m-28=0 ~~~--\ \textgreater \ onde~\boxed{ \frac{-b\pm \sqrt{b\²-4ac} }{2a}} \\ a=1 \\ b=-12 \\ c=-28 \\ substituindo: \\ m= \frac{12\pm \sqrt{(-12)\²-4.(1).(-28)} }{2.(1)}$

$m= \frac{12\pm16}{2}=\ \textgreater \ \begin{cases}m_1=14 \\ \\ m_2=-2\end{cases} \\ \\ Por~tanto~os~valores~que~pode~ter~(m)~e' \\ \\ \bigg\{14;-2\bigg\} \\ \\ \mathbb{xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx}\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Espero~ter~ajudado!!$