The point (0, 5) lies on a circle that is centered at the origin. Does (–3, –4) also lie on the circle?

(-3, -4) does indeed also lie on the circle.

Step-by-step explanation:

If the center of the given circle is (0, 0), and the radius of the circle is 5 (which is the distance from the center (0, 0) to the given point (0, 5), then the equation of the circle is

x^2 + y^2 = 5^2.  We ask whether the point (-3, -4) satisfies this equation.

(-3)^2 + (-4)^2 = 25, or

9 + 16 = 25.  This equation is true, so (-3, -4) does indeed also lie on the circle.