Respuesta :
Given that a rectangle has vertices J(3, 3), K(9, 3), L(9, 6), and M(3, 6).
We need to determine the coordinates of the rectangle after dilating from the origin by a scale factor of [tex]\frac{2}{3}[/tex]
Dilation of the coordinates J(3, 3):
To dilate the coordinates J(3, 3), we shall multiply it with the factor of [tex]\frac{2}{3}[/tex]
Thus, we have;
[tex]J(3,3) \rightarrow J^{\prime}\left(\frac{2}{3}(3), \frac{2}{3}(3)\right) \rightarrow J^{\prime}(2,2)[/tex]
Thus, the coordinates after dilation is J'(2,2)
Dilation of the coordinates K(9,3):
To dilate the coordinates K(9,3), we shall multiply it with the factor of [tex]\frac{2}{3}[/tex]
Thus, we have;
[tex]K(9,3) \rightarrow K^{\prime}\left(\frac{2}{3}(9), \frac{2}{3}(3)\right) \rightarrow K^{\prime}(6,2)[/tex]
Thus, the coordinates after dilation is K'(6,2)
Dilation of the coordinates L(9,6):
To dilate the coordinates L(9,6), we shall multiply it with the factor of [tex]\frac{2}{3}[/tex]
Thus, we have;
[tex]L(9,6) \rightarrow L^{\prime}\left(\frac{2}{3} (9), \frac{2}{3} (6)\right) \rightarrow L^{\prime}(6,4)[/tex]
Thus, the coordinates after dilation is L'(6,4)
Dilation of the coordinates M(3,6):
To dilate the coordinates M(3,6), we shall multiply it with the factor of [tex]\frac{2}{3}[/tex]
Thus, we have;
[tex]M(3,6) \rightarrow M^{\prime}\left(\frac{2}{3} (3), \frac{2}{3} (6)\right) \rightarrow M^{\prime}(2,4)[/tex]
Thus, the coordinates after dilation is M'(2,4)
Hence, the coordinates of the rectangle after dilation are J'(2,2), K'(6,2), L'(6,4) and M'(2,4)
