Circle Geometry and Properties

The video tutorial demonstrates how to graph circles using given center coordinates and radius. It starts with a circle centered at (3, -2) with a radius of 5 units, showing how to adjust the radius using a widget. The tutorial then moves on to graph another circle centered at (-4, 1) with a point (0, 4) on it, explaining how to adjust the radius to include the point. The video emphasizes understanding the relationship between the center, radius, and points on the circle.

What is the center of the circle described in the introduction?

• (-3, 2)

• (0, 0)

• (2, -3)

• (3, -2)

What is the radius of the circle in the introduction?

• 10 units

• 7 units

• 5 units

• 3 units

What tool is used to adjust the circle's center and radius?

• A ruler

• A widget

• A compass

• A protractor

What is the new center of the circle in the second example?

• (4, -1)

• (-4, 1)

• (1, -4)

• (0, 4)

Which point must be included on the circle in the second example?

• (4, 0)

• (0, 0)

• (1, 1)

• (0, 4)

What is the radius of the circle after adjusting to include the point (0, 4)?

• 5 units

• 3 units

• 4 units

• 6 units

How do you verify the radius of the circle?

• By checking the circumference

• By measuring the diameter

• By using a protractor

• By calculating the distance from the center to a point on the circle

What is the x-coordinate of the center in the verification section?

• -4

• 0

• 1

• 4

What is the y-coordinate of the center in the verification section?

• -1

• 0

• 1

• 4

What is the distance from the center to the point (1, 1) on the circle?

• 3 units

• 4 units

• 5 units

• 6 units