Question

Does the point (-10,3) lie on the circle that passes through the point(-2,9) with center (-3,2)?

Answer 1

Answer:

D) Yes, the radius and distance are equal.

Step-by-step explanation:

1. Find the radius (distance formula): √((-2 + 3)² + (9 - 2)²) = √(1 + 49) = √50 = 5√2. A and C can not be the answer because the reasoning is wrong.

2. Find the distance from the center to the point (distance formula):

√((-10 + 3)² + (3 - 2)²) = √(49 + 1) = √50 = 5√2.

By the definition of a circle, point (-10, 3) is part of the circle because its distance from the center is equal to the radius.

Answer 2

Answer:

Yes, last answer is correct

Step-by-step explanation:

Circle is a set of points that have the same distance to the center (radius). You can calculate the radius in both cases. Distance between the center (-3,2) and the given point (-2,9) is sqrt((-3+2)^2+(2-9)^2) = sqrt(50) = 5sqrt(2). When you check the point in question (-10, 3), the distance is sqrt((-10+3)^2+(3-2(^2) = sqrt(50) = 5sqrt(2). Distance is the same so this point is on the circle (all the points with this distance from the center will be on the circle)