Question Number 200249 by Calculusboy last updated on 16/Nov/23
$$\boldsymbol{{Solve}}:\:\:\boldsymbol{{find}}\:\boldsymbol{{the}}\:\boldsymbol{{distance}}\:\boldsymbol{{of}}\:\boldsymbol{{the}}\:\boldsymbol{{point}}\:\boldsymbol{{P}}\left(\mathrm{3},\mathrm{4}\right)\:\boldsymbol{{from}}\:\boldsymbol{{the}}\:\boldsymbol{{line}}\:\boldsymbol{{y}}=−\mathrm{2}\boldsymbol{{x}}+\mathrm{3} \\ $$
Commented by mr W last updated on 18/Nov/23
Answered by Frix last updated on 16/Nov/23
$$\mathrm{Besides}\:\mathrm{I}\:\mathrm{really}\:\mathrm{think}\:\mathrm{you}\:\mathrm{should}\:\mathrm{not}\:\mathrm{post}\:\mathrm{questions}\:\mathrm{or}\:\mathrm{answers}\:\mathrm{or}\:\mathrm{comments}\:\mathrm{in}\:\mathrm{single}\:\mathrm{lines}\:\mathrm{here}'\mathrm{s}\:\mathrm{the}\:\mathrm{general}\:\mathrm{answer}\:\mathrm{to}\:\mathrm{your}\:\mathrm{question};\:\mathrm{just}\:\mathrm{insert}\:\mathrm{the}\:\mathrm{values}.\:\mathrm{In}\:\mathbb{R}^{\mathrm{2}} \:\mathrm{the}\:\mathrm{distance}\:\mathrm{between}\:\mathrm{a}\:\mathrm{given}\:\mathrm{line}\:{l}:\:{ax}+{by}+{c}=\mathrm{0}\:\mathrm{and}\:\mathrm{a}\:\mathrm{given}\:\mathrm{point}\:{P}=\left({p},\:{q}\right)\:\mathrm{is}\:\mid{lP}\mid=\frac{\mid{ap}+{bq}+{c}\mid}{\:\sqrt{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} }}. \\ $$
Commented by Calculusboy last updated on 16/Nov/23
$$\boldsymbol{{okay}}\:\boldsymbol{{sir}} \\ $$
Commented by mr W last updated on 18/Nov/23
$${just}\:{say}\:{okay}\:{is}\:{not}\:{enough},\:{you} \\ $$$${should}\:{also}\:{act}! \\ $$