$ ext{Suppose you have a unit circle centered at the origin in the coordinate plane. You flip the unit circle over the y-axis. Determine the coordinates of a point } (x, y) ext{ on the original unit circle after the transformation, given that } x^2 +
Answer 1
Henry Green
$\text{Given the equation of the original unit circle}$
$x^2 + y^2 = 1.$
$\text{When the unit circle is flipped over the y-axis, each point } (x, y) \text{ is transformed to } (-x, y).$
$\text{So, the new coordinates after transformation are } (-x, y).$
$\text{For instance, if you have a point } (x, y) = (\frac{1}{2}, \frac{\sqrt{3}}{2}) \text{ on the original unit circle, the transformed coordinates are:}$
$(-\frac{1}{2}, \frac{\sqrt{3}}{2}).$
Answer 2
John Anderson
$ ext{The equation of the original unit circle is}$
$x^2 + y^2 = 1.$
$ ext{When the unit circle is flipped over the y-axis, a point } (x, y) ext{ on the unit circle transforms to } (-x, y).$
$ ext{For example, consider the point } (frac{3}{5}, frac{4}{5}) ext{ on the original unit circle. After transformation, the new coordinates are:}$
$(-frac{3}{5}, frac{4}{5}).$
Answer 3
Emma Johnson
$ ext{The transformation of the unit circle over the y-axis changes a point } (x, y) ext{ to } (-x, y).$
$ ext{For example, if a point on the original circle is } (frac{2}{3}, frac{sqrt{5}}{3}), ext{ the transformed point is:}$
$(-frac{2}{3}, frac{sqrt{5}}{3}).$
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