Question

Is the point (12, 12) on the unit circle?(1 point) Responses Yes Yes No No Question 2 Explain how you know if (12, 12) is on the unit circle by either: a) Explaining in words or b) Showing the mathematical steps that led to your answer

Answer 1

To determine if the point (12, 12) is on the unit circle, we need to understand the definition of the unit circle. The unit circle is defined as the set of all points (x, y) in a Cartesian plane that satisfy the equation:

\[
x^2 + y^2 = 1
\]

Now, let's check if the point (12, 12) satisfies this equation:

1. Substitute x = 12 and y = 12 into the equation:

\[
12^2 + 12^2
\]

2. Calculate \(12^2\):

\[
12^2 = 144
\]

3. Therefore:

\[
12^2 + 12^2 = 144 + 144 = 288
\]

4. Now compare this result with 1:

\[
288 \neq 1
\]

Since \(288\) does not equal \(1\), the point (12, 12) is not on the unit circle.

### Answer
No, the point (12, 12) is not on the unit circle.

### Explanation
The unit circle consists of points where the sum of the squares of the coordinates equals 1. For (12, 12), the sum of the squares is 288, which is not equal to 1, thus confirming that the point is not on the unit circle.