Ailani draws a map of her local town. She places the town hall at the origin of a coordinate plane and represents a lake with a circle drawn on the map. The center of the lake is 19 miles east and 3 miles south of the town hall, and the radius of the lake is 0.5 miles.If the positive x-axis represents east and the positive y-axis represents north, which equation represents the lake?
Answer
A
(x + 19)2 + (y – 3)2 = 0.5
B
(x – 19)2 + (y + 3)2 = 0.5
C
(x + 19)2 + (y – 3)2 = 0.25
D
(x – 19)2 + (y + 3)2 = 0.25
Explanation
A circle with center (h, k) and radius r has equation (x − h)² + (y − k)² = r². The lake’s center is (19, −3), since east is positive x and south is negative y, and its radius squared is 0.5² = 0.25. Substituting gives (x − 19)² + (y + 3)² = 0.25, choice D.
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