Question

Consider ADEF with vertices D(-6,4) E(0,8), and F(2,-2) Find the coordinates of the vertices of the final image of ADEF after the similarity transformation Translation: (x,y) - (x + 8y + 4) Dilation: (x,y)-(1/2x, 1/2y) centered at (0,0) The coordinates of the vertices of the final image are D'' E" and F"

Answer 1

D''(1, 4), E"(4, 6) and F"​(5, 1)

Step-by-step explanation:

Coordinates of original image: D(-6,4), E(0,8) and F(2,-2)

Translation: (x,y) to (x + 8, y + 4)

The coordinate becomes:

D(-6,4) = (-6+8, 4+4) = (2, 8)

E(0,8) = (0+8, 8+4) = (8, 12)

F(2,-2) = (2+8, -2+4) = (10, 2)

Dilation: (x,y) to (1/2x, 1/2y) centered at (0,0)

D" = (2, 8) to 1/2(2), 1/2(8) = (1, 4)

E" = (8, 12) to 1/2(8), 1/2(12) = (4, 6)

F" = (10, 2) to 1/2(10), 1/2(2) = (5, 1)

The coordinates of the vertices of the final image are D''(1, 4), E"(4, 6) and F"​(5, 1)