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Math  /  Geometry

QuestionFind the point symmetric to [72,π3]\left[\frac{7}{2}, \frac{\pi}{3}\right] about the yy-axis. [−7,2π3]\left[-7, \frac{2 \pi}{3}\right] [72,2π3]\left[\frac{7}{2}, \frac{2 \pi}{3}\right] [72,5π6]\left[\frac{7}{2}, \frac{5 \pi}{6}\right] [−72,π3]\left[-\frac{7}{2}, \frac{\pi}{3}\right] [7,2π3]\left[7, \frac{2 \pi}{3}\right]

Studdy Solution

STEP 1

1. The point given is [72,π3]\left[\frac{7}{2}, \frac{\pi}{3}\right].
2. We need to find the point symmetric to this point about the yy-axis.

STEP 2

1. Understand symmetry about the yy-axis.
2. Apply the symmetry transformation.
3. Identify the symmetric point.

STEP 3

Understand symmetry about the yy-axis:
- When a point (x,y)(x, y) is reflected over the yy-axis, the xx-coordinate changes sign, while the yy-coordinate remains the same.

STEP 4

Apply the symmetry transformation:
- Given the point [72,π3]\left[\frac{7}{2}, \frac{\pi}{3}\right], reflect it over the yy-axis by changing the sign of the xx-coordinate:
(−72,π3) \left(-\frac{7}{2}, \frac{\pi}{3}\right)

STEP 5

Identify the symmetric point:
- The point symmetric to [72,π3]\left[\frac{7}{2}, \frac{\pi}{3}\right] about the yy-axis is [−72,π3]\left[-\frac{7}{2}, \frac{\pi}{3}\right].
The symmetric point is:
[−72,π3] \boxed{\left[-\frac{7}{2}, \frac{\pi}{3}\right]}

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