Using the Distance Formula to Verify Points on a Circle

This video tutorial explains how to determine if a point is on a circle by using the distance formula. It begins with a review of the distance formula derived from the Pythagorean theorem. The tutorial then demonstrates how to find the radius of a circle when given a center and a point on the circle. It also covers how to test whether a point is on or outside a circle by calculating the distance from the center and comparing it to the radius. The lesson concludes with verifying points using the distance formula.

What is the primary mathematical concept used to derive the distance formula?

• Pythagorean Theorem

• Quadratic Equation

• Algebraic Expressions

• Trigonometric Identities

If you have two points (3, 2) and (7, 5), what is the distance between them?

• 6

• 5

• 4

• 7

What is the result of squaring the difference between two coordinates in the distance formula?

• It gives a component of the distance

• It gives the area

• It gives the radius

• It gives the circumference

How can you find the radius of a circle if you know the center and a point on the circle?

• By using the volume formula

• By using the circumference formula

• By using the distance formula

• By using the area formula

Given a circle with center (2, 3) and radius 5, is the point (-2, 6) on the circle?

• No, because the distance is 7

• Yes, because the distance is 4

• No, because the distance is 6

• Yes, because the distance is 5

What is the distance between the center (2, -4) and the point (7, 3) if the radius is sqrt(61)?

• sqrt(25)

• sqrt(49)

• sqrt(61)

• sqrt(74)

If a point is further from the center than the radius, where is it located relative to the circle?

• Outside the circle

• On the circle

• Inside the circle

• At the center of the circle