Question

A circle is centered at O (0,0) and has a radius of √53. Where does the point V(-3,-7) lie?

A) Inside the circle
B) On the circle
C) Outside the circle

Answer 1

The point V(-3, -7) lies outside the circle centered at O (0,0) with a radius of √53.

Step-by-step explanation:

The point V(-3, -7) can be plotted on a coordinate system with the x-coordinate -3 and the y-coordinate -7. To determine where the point lies in relation to the circle centered at O (0,0) with a radius of √53, we can calculate the distance between the point and the center of the circle using the distance formula. The distance between the two points can be calculated as:

d = √((x2 - x1)^2 + (y2 - y1)^2)

d = √((-3 - 0)^2 + (-7 - 0)^2)

d = √((-3)^2 + (-7)^2)

d = √(9 + 49)

d = √58

The distance is greater than the radius of the circle (√53), so the point V(-3, -7) lies outside the circle.