Hexagon IJKLMN is dilated by a scale factor of two fifths from the origin to create hexagon I'J'K'L'M'N' then N' is [tex]\left(\dfrac{-12}{5},\dfrac{4}{5}\right)[/tex] and this can be determine by multilying the dilation factor to the coordinates of IJKLMN.
Given :
- Hexagon IJKLMN.
- Points - I(-2,6), J(4,4), K(6,-1), L(-1,2), M(-4,-4), and N(-6,2).
If hexagon IJKLMN is dilated by a scale factor of two fifths from the origin to create hexagon I'J'K'L'M'N' then points I'J'K'L'M'N' will be:
[tex]\rm I' - \left(-2\times\dfrac{2}{5},6\times \dfrac{2}{5} \right)=\left(\dfrac{-4}{5},\dfrac{12}{5}\right)[/tex]
[tex]\rm J' - \left(4\times\dfrac{2}{5},4\times \dfrac{2}{5} \right)=\left(\dfrac{-8}{5},\dfrac{8}{5}\right)[/tex]
[tex]\rm K' - \left(6\times\dfrac{2}{5},-1\times \dfrac{2}{5} \right)=\left(\dfrac{12}{5},\dfrac{-2}{5}\right)[/tex]
[tex]\rm L' - \left(-1\times\dfrac{2}{5},2\times \dfrac{2}{5} \right)=\left(\dfrac{-2}{5},\dfrac{4}{5}\right)[/tex]
[tex]\rm M' - \left(-4\times\dfrac{2}{5},-4\times \dfrac{2}{5} \right)=\left(\dfrac{-8}{5},\dfrac{-8}{5}\right)[/tex]
[tex]\rm N' - \left(-6\times\dfrac{2}{5},2\times \dfrac{2}{5} \right)=\left(\dfrac{-12}{5},\dfrac{4}{5}\right)[/tex]
Therefore, if hexagon IJKLMN is dilated by a scale factor of two fifths from the origin to create hexagon I'J'K'L'M'N' then N' is [tex]\left(\dfrac{-12}{5},\dfrac{4}{5}\right)[/tex] .
For more information, refer the link given below:
https://brainly.com/question/4700458
