Find one path to move the following triangle ABC onto its image triangle A’B’C’ below. In narrative form, give each transformation and describe the resulting image in relationship to the previous one. Assignment: Transformations and DilationAt the end of Lecture 6.3, a series of functions (reflection, translation, rotation, and dilation)were used to transform a quadrilateral ABCD onto an image A'B'C'D'.We discussed that there was more than one sequence to move the geometric figure onto itsimage. Find one path to move the following triangle ABC onto its image triangle A'B'C' below.Also, in narrative form, give each transformation and describe the resulting image inrelationship to the previous one.14+12-108--6-BCA'C10B'

Given: ( The coordinates of the triangle ABC - A = (1,1) B = (4,3) C = (4,1) The coordinates of the triangle A'B'C' - A' = (8,11) B' = (12,5) C' = (8,5) Path to move the triangle ABC onto image A'B'C' Rotation → Dilation → Translation 1. Rotation ABC is rotated by 90 degrees. A = (1,1)→(1, -1) B = (4,3)→(3,-4) C = (4,1)→(1,-4) 2. Dilation Length of BC = 2 Length of B'C' = 4 So, the dilation factor is k=LB'C'LBC=42=2 A = (1,-1)→(2, -2) B = (3,-4)→(6,-8) C = (1,-4)→(2,-8) 3. Translation Image shifted 6 units to the right and 13 units to the upward. ∴x,y→x+6,y+13 A= (2,-2)→(8, 11)=A' B = (6,-8)→(12,5)=B' C = (2,-8)→(8,5)=C'In narrative form, the transformation takes place as triangle ABC is rotated by 90 degrees in clockwise direction, then diluted by scale factor of 2 and then translated by 6 units to the right and 13 units to the upward to obtain the image A'B'C'. Answer: Transformation of triangle ABC to image A'B'C' Rotation - 90 degrees clockwise Dilation - Scale factor of 2 Translation - 6 units to the right and 13 units to the upward.