What is the scale factor of the dilation of line segment BA?A) 1/5B) 1/4C) 4D) 5

Accepted Solution

Answer: The correct option is D, i.e., 5.Explanation:Dilation is defined as the enlargement or compression of a figure along the center of dilation according to the scale factor k.If k>1 then it shows the enlargement and if 0<k<1 then it shows the compression.If k is negative the image and preimage lies on the opposite sides of center of dilation.The image and preimage are similar to each other and the sides are in the proportion of k.In the given figure the length of side CA is 4 unit.The image of CA is CA' and its length is,[tex]CA"=CA+AA'=4+16=20[/tex]Since the given figure shows the enlargement, so k>1.[tex]k=\frac{\text{distance of preimage from center}}{\text{distance of image from center}}[/tex][tex]k=\frac{CA'}{CA}[/tex][tex]k=\frac{20}{4} =5[/tex]Therefore, the value of k is 5 and D is the correct option.