Find the reflected image of a point across the x-axis, y-axis, and origin, and understand invariant points.
Reflecting a point (x,y) across the x-axis gives (x,−y). Reflecting across the y-axis gives (−x,y). Reflecting across the origin gives (−x,−y).
Find the reflection of (3, 5) in the x-axis.
(3, −5)
Find the reflection of (−4, 2) in the y-axis.
(4, 2)
A point that maps to itself under a reflection is called invariant. Points on the x-axis are invariant under reflection in the x-axis, and similarly for the y-axis.
Is the point (5, 0) invariant under reflection in the x-axis?
Yes, since reflecting (5,0) in the x-axis gives (5,−0)=(5,0), unchanged
Is the point (0, 4) invariant under reflection in the y-axis?
Yes, since reflecting (0,4) in the y-axis gives (−0,4)=(0,4), unchanged
1. Find the reflection of (6, −2) in the x-axis.
2. Find the reflection of (−3, −7) in the y-axis.
3. Find the reflection of (4, 5) in the origin.
4. Is the point (0, 0) invariant under all reflections (x-axis, y-axis, origin)?
5. Which points are invariant under reflection in the x-axis?