The point (2√2, 2√2) does not lie on the unit circle since a unit circle has a radius of 1 and points on it would be of the form (cos(θ), sin(θ)) where cos²(θ) + sin²(θ) = 1.
In fact, the coordinates (2√2, 2√2) corresponds to a point that is outside the unit circle.
However, if we were to consider the coordinates correctly situated within a system where the shape intersects at points according to the unit circle's properties (rather than suggesting this point exists on the unit circle), we should refer to the special right triangles.
The correct interpretation here is that if we had a special right triangle formed by a unit circle:
- A 45-45-90 triangle has vertices (1,1), (1,-1), (-1,1), etc., lying at equivalent angles to the axes.
- A 30-60-90 triangle would have different ratios and typically would not intersect at point coordinates corresponding to the unit circle's intersection.
That said, since the options are to choose from, with (2√2, 2√2) indicating angles of 45 degrees in a general sense reflected in its slope (2:2), the correct answer regarding a special right triangle whose angles yield symmetrical results in a 1:1 ratio is a 45-45-90 triangle.
Therefore, the response is:
a 45-45-90 triangle.
1 answer