What  is  an  equation  for  the  translation  of  (x  –  2)2 +  (y  +  1)2   =  16    by  3  units  left and  5  units  up?

( x + 1)² + (y - 4)² = 16

Explanation:

1) The given equation,  ( x - 2)² + (y + 1)² = 16, represents a circumference with center (2,-1) and radius √16 = 4.

1) The translation will not modify the radius of the circunference, siince translations are rigid transformations.

2) The translation 3 units to the left and 5 units upward certainly will move the center of the circunference.

This is how:

(x,y) → (x - 3, y + 5)

(2, -1) → (2 - 3, - 1 + 5) = (- 1, 4)

3) Then, keeping the same radius and being the center (-1,4), the equation of the circumference after the translation will be:

( x + 1)² + (y - 4)² = 16 ← answer

the image of (6, 9) under a dilation is (4, 6). the scale factor is

b. 2/3