A coordinate system is placed at the center of a house with the positive x-axis pointing east, and the positive y-axis pointing north. A pest-deterrent device that uses high-frequency sound waves is Placed in an electrical outlet 15 ft west and 8 ft south of the center of the house. If the device has a Range of 11 feet, write an inequality that represents the points on the coordinate system affected by The device.
A) $( x - 15 ) ^ { 2 } + ( y - 8 ) ^ { 2 } \geq 11$
B) $( x - 15 ) ^ { 2 } + ( y - 8 ) ^ { 2 } \leq 121$
C) $( x + 15 ) ^ { 2 } + ( y + 8 ) ^ { 2 } \leq 121$
D) $( x - 15 ) ^ { 2 } + ( y - 8 ) ^ { 2 } \leq 11$

Question

A coordinate system is placed at the center of a house with the positive x-axis pointing east, and the positive y-axis pointing north. A pest-deterrent device that uses high-frequency sound waves is Placed in an electrical outlet 15 ft west and 8 ft south of the center of the house. If the device has a Range of 11 feet, write an inequality that represents the points on the coordinate system affected by The device. 
A) $( x - 15 ) ^ { 2 } + ( y - 8 ) ^ { 2 } \geq 11$
B) $( x - 15 ) ^ { 2 } + ( y - 8 ) ^ { 2 } \leq 121$
C) $( x + 15 ) ^ { 2 } + ( y + 8 ) ^ { 2 } \leq 121$
D) $( x - 15 ) ^ { 2 } + ( y - 8 ) ^ { 2 } \leq 11$

Quizplus · Accepted Answer

The device is located 15 ft west and 8 ft south of the center, so its coordinates are (-15, -8). The range of the device is 11 feet, which is the radius of the circle of effect. The equation for a circle is $(x - h)^2 + (y - k)^2 = r^2$, where (h, k) is the center and r is the radius. Substituting the given values, we get $(x + 15)^2 + (y + 8)^2 = 11^2$, which simplifies to $(x + 15)^2 + (y + 8)^2 \leq 121$, since the inequality represents all points within the range of the device, including the boundary.

A Coordinate System Is Placed at the Center of a House