Witch of the following dilations was applied to ABCD to create AB’C’D’?

Accepted Solution

Answer:Scale factor = [tex]\frac{2}{3}[/tex]Step-by-step explanation:Let x be scale factor.Since we know that the dilation of a figure changes all the sides of figure with same scale factor.  Let us find scale factor of dilation applied to quadrilateral ABCD to create AB'C'D'.Let us find side length of AD and AD' using distance formula.[tex]\text{Distance}=\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}}[/tex][tex]\text{Length of AD}=\sqrt{(1-1)^{2}+(4-7)^{2}}[/tex][tex]\text{Length of AD}=\sqrt{(0)^{2}+(-3)^{2}}[/tex][tex]\text{Length of AD}=\sqrt{9}=3[/tex]Now let us find length of side AD'. [tex]\text{Length of AD'}=\sqrt{(1-1)^{2}+(5-7)^{2}}[/tex][tex]\text{Length of AD'}=\sqrt{(0)^{2}+(-2)^{2}}[/tex] [tex]\text{Length of AD'}=\sqrt{4}=2[/tex] The scale factor (x) times the length of AD will be length of AD'.[tex]3\cdot x=2[/tex] [tex]x=\frac{2}{3}[/tex]Therefore, dilation by a scale factor of 2/3 is applied to ABCD to create AB'C'D'.