What is the equation for the translation of x2 + y2 = 16 seven units to the right and five units up?
(x + 7)2 + (y – 5)2 = 16
(x - 7)2 + (y + 5)2 = 16
(x + 7)2 + (y + 5)2 - 16
(x - 72 + (y – 5)2 = 16

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Step-by-step explanation:

The given circle has equation .

This is the equation that has its center at the origin with radius 4 units.

When this circle is translated seven units to the right and five units up, then the center of the circle will now be at (7,5).

The equation of a circle with center (h,k) and radius r units is .

This implies that, the translated circle will now have equation.

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g = (2, 2)

step-by-step explanation:

given the ratio is 1 : 1 then f is the midpoint of eg

let the coordinates of g = (x, y)

using the midpoint formula

(0 + x) = 1 ( multiply both sides by 2 )

0 + x = 2 ⇒ x = 2

similarly

(4 + y) = 3 ( multiply both sides by 2 )

4 + y = 6 ( subtract 4 from both sides )

y = 2

coordinates of g = (2, 2)