The smaller triangle is a pre-image of the bigger triangle. The center of dilation is (2, −2).What is the scale factor used to create the dilation?3​ 13 ​​−13 ​−3

Answer: The correct option is fourth option, i.e., -3.Explanation:It is given that the smaller triangle is a preimage of the bigger triangle. The center of dilation is (2, −2).From the given figure it is noticed that the vertices of preimage are A(2,-2), B(2,2), C(-2,-2) and the vertices of preimage are A'(2,-2), B'(2,-14) and C'(14,-2).The length of AB is 4 and the length of A'B' is 12.The sides of image and preimage are in proportion.proportion = [tex]\frac{12}{4} =3[/tex]Since the image is enlargement of preimage therefore k>1 and k<-1.Since the image and preimage are lies in opposite sides of center of dilation, therefore the scale factor must be negative.[tex]k=-3[/tex]There correct option is option 4.