Which point is on the circle centered at the origin with a radius of 5 units?

To find a point that lies on a circle centered at the origin with a radius of 5 units, we can use the equation of a circle:

x² + y² = r²

Here, r is the radius of the circle. In this case, r = 5, so the equation becomes:

x² + y² = 25

Any point (x, y) that satisfies this equation will be on the circle. For example:

• If we take x = 3, we can find y by solving:

x² + y² = 25 → 3² + y² = 25 → 9 + y² = 25 → y² = 16 → y = ±4

• This gives us two points: (3, 4) and (3, -4).

Similarly, if we take x = 0, we can find:

y² = 25 → y = ±5

• This gives us the points: (0, 5) and (0, -5).

Another example is if we take x = 5:

y² = 0 → y = 0

• This gives us the point: (5, 0).

In conclusion, any point (x, y) that satisfies the equation x² + y² = 25 lies on the circle centered at the origin with a radius of 5 units. Some examples of such points are (3, 4), (3, -4), (0, 5), (0, -5), and (5, 0).