Respuesta :
Answer: The area of C'D'E' = 1/4 × the area of CDE
Step-by-step explanation:
Let the coordinates of triangle CDE are [tex](x_1,y_1)[/tex], [tex](x_2, y_2)[/tex] and [tex](x_3,y_3)[/tex]
Since, In the dilation about origin by the scale factor k,
[tex](x,y) \rightarrow (kx,ky)[/tex]
Thus, when triangle CDE is dilated by a scale factor [tex]\frac{1}{k}[/tex]
Then the coordinates of triangle C'D'E' are,
[tex](\frac{x_1}{2},\frac{y_1}{2})[/tex],[tex](\frac{x_2}{2},\frac{y_2}{2})[/tex] and [tex](\frac{x_3}{2},\frac{y_3}{2})[/tex]
Since, the area of triangle C'D'E'
= [tex]\frac{1}{2} [\frac{x_1}{2} (\frac{y_2}{2} - \frac{y_3}{2}) + \frac{x_2}{2} (\frac{y_3}{2} - \frac{y_1}{2})+\frac{x_3}{2} (\frac{y_1}{2} - \frac{y_2}{2})][/tex]
= [tex]\frac{1}{4}[\frac{1}{2}(x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)][/tex]
= [tex]\frac{1}{4} \times \text{ area of triangle CDE}[/tex]
