Answer: ( 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
