Question

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? (x 19)2 (y – 3)2 = 0. 5 (x – 19)2 (y 3)2 = 0. 5 (x 19)2 (y – 3)2 = 0. 25 (x – 19)2 (y 3)2 = 0. 25.

Answer 1

The equation representing the lake on the coordinate plane, considering the town hall as the origin, is (x - 19)^2 + (y + 3)^2 = 0.25.

Step-by-step explanation:

If Ailani draws a map with the town hall at the origin of a coordinate plane, and a lake that is 19 miles east and 3 miles south of the town hall defines the center of a circle with a radius of 0.5 mile, the lake will be represented by a circular equation on the coordinate plane. Given that the positive x-axis represents east and the positive y-axis represents north, the center of the lake will be at (19, -3). The radius of the lake is 0.5 miles, so the equation of the circle is (x - 19)2 + (y + 3)2 = r2, where r is the radius. Thus, the correct equation with the radius squared (0.5)2 which equals 0.25 is (x - 19)2 + (y + 3)2 = 0.25.