Distance and Radius in Geometry

The video tutorial explores a circle-related word problem involving a cell phone tower with a 12-mile radius. The tower is located at (-3, 5) on a coordinate plane. The tutorial guides viewers through writing the standard equation of the circle and determining if a point (8, 0) is within the coverage area using the distance formula. The calculated distance is 12.08 miles, slightly outside the 12-mile radius, indicating the point is outside the service range.

What is the radius of the service area for the cell phone tower?

• 20 miles

• 12 miles

• 15 miles

• 10 miles

Where is the cell phone tower located on the coordinate plane?

• (0, 0)

• (-3, 5)

• (3, -5)

• (5, -3)

What is the standard form of the equation for a circle centered at (-3, 5) with a radius of 12?

• (x - 3)^2 + (y - 5)^2 = 144

• (x + 3)^2 + (y + 5)^2 = 144

• (x + 3)^2 + (y - 5)^2 = 144

• (x - 3)^2 + (y + 5)^2 = 144

What is the radius of the circle in the standard equation derived in the video?

• 16 miles

• 14 miles

• 12 miles

• 10 miles

Which formula is used to determine the distance between two points on a coordinate plane?

• Slope formula

• Midpoint formula

• Quadratic formula

• Distance formula

What is the distance between the center of the circle and the point (8, 0)?

• 13 miles

• 12.08 miles

• 10.5 miles

• 11.5 miles

If the distance from the center to a point is greater than the radius, where is the point located?

• On the circle

• Inside the circle

• Outside the circle

• At the center

What is the calculated distance from the center to the point (8, 0) in the video?

• 11.5 miles

• 12 miles

• 12.08 miles

• 12.5 miles

Is the point (8, 0) within the service range of the cell phone tower?

• It is at the center

• No, it is outside the range

• It is exactly on the boundary

• Yes, it is within the range

What is the significance of the distance 12.08 miles in the context of the video?

• It is the diameter of the circle

• It is the circumference of the circle

• It is the distance from the center to the point (8, 0)

• It is the radius of the circle