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When baking cookies, each cookie should be placed about 2 inches from one another to allow room to expand. If one cookie has a radius of 1 inch and a center at C(1, –1), find the center and equation of the cookie immediately to the right. (Assume that each cookie is uniform with a radius of 1 inch and that 1 inch = 1 unit on a coordinate plane.)

Respuesta :

Edufirst

Answer:



Center: (1, 3)


Equation: (x - 1)² + (y - 3)² = 1



Explanation:



1) The initial distance between the centers of two adjacent cookies must be equal to the separation indicated (2 inches) plus the radius of each cookie, which is 2 × 1 in.


So, the separation of the centers is 2 in + 2 × 1 in = 2in + 2 in = 4 in.


2) Then the coordinates of the center the cookie to the right of the given cookie are (1, -1 + 4) = (1, 3).


3) The equation of the circle of radius r and center (a,b) is:


(x - a)² + (y - b)² = r²


So, using a = 1, b = 3, and r = 1, you get:


(x - 1)² + (y - 3)² = 1


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