Understanding Circles and Their Properties

The video tutorial explains how to determine the center of a circle and calculate its radius using the distance formula. It starts by identifying the center coordinates and a point on the circle. The radius is defined as the distance between these two points. The tutorial then applies the distance formula, which is based on the Pythagorean theorem, to calculate the radius. Changes in x and y coordinates are computed, and the radius is finalized by squaring these changes and taking the square root of their sum.

What are the coordinates of the center of the circle?

• (-4, -7)

• (-7, -4)

• (4, 7)

• (7, 4)

Which point is mentioned as being on the circle?

• (-5, 9)

• (5, -9)

• (-9, 5)

• (9, -5)

What is the radius of a circle?

• The distance from the center to any point on the circle

• The circumference of the circle

• The diameter of the circle

• The area of the circle

Which formula is used to calculate the distance between two points?

• Quadratic formula

• Area formula

• Pythagorean theorem

• Volume formula

What is the change in x when moving from the center to the point (-5, 9)?

• -9

• 1

• 9

• -1

What is the change in y when moving from the center to the point (-5, 9)?

• -2

• 16

• 2

• -16

What is the value of the radius squared?

• 10

• 25

• 50

• 5

What is the final calculated radius of the circle?

• Square root of 5

• Square root of 50

• Square root of 10

• Square root of 25

Why does the negative sign not matter when calculating the distance?

• Because it is squared

• Because it is ignored

• Because it is subtracted

• Because it is added

What is the significance of the distance formula in this context?

• It helps find the radius of the circle

• It calculates the area of the circle

• It measures the circumference of the circle

• It determines the diameter of the circle