Does the point ( 3 , 3 ) lie on the circle that is centered at the origin and contains the point (3, 0)? why?

If the center is at point (0,0) which is the origin and point (3,0) is along the circle, then that means the radius is 3 units. Now, let's find if point (3,3) is equal to the radius by using the distance formula. Let point 1 be (0,0) and point 2 be (3,3).

d = √[(x₂ - x₁)² + (y₂ - y₁)²]
d = √[(3 - 0)² + (3 - 0)²]
d = 4.24 units

Since the distance is more than the length of radius, it means that point (3,3) lies outside the circle.