X-AXIS REFLECTIONS
What happens to the y-value when reflecting over the x-axis?
It becomes the opposite (sign changes)
What changes when reflecting over the y-axis?
The x-value changes sign
Is reflecting over both axes the same as a 180° rotation?
Yes
What line is used for reflection if x-values change sign?
y-axis (x = 0)
Point (1,1) reflected over x-axis and stays on same x-value. True or false?
True
Reflect (3, 4) over the x-axis.
(3, −4)
Reflect (4, 3) over the y-axis.
(−4, 3)
What happens to (x, y) after reflection over BOTH axes?
(−x, −y)
What line is used if y-values change sign?
x-axis (y = 0)
Why does reflection change orientation but not shape?
Because distance and size stay the same
Reflect (−2, 5) over the x-axis.
(−2, −5)
Reflect (−6, 2) over the y-axis.
(6, 2)
Reflect (2, 3) over x-axis, then y-axis.
(−2, −3)
Reflect (3, 5) over y = 0 (x-axis)
(3, −5)
A shape is reflected over y-axis. What changes?
Left/right position (x-values)
A point is (0, −7). After reflection over x-axis, what is it?
(0, 7)
Point (0, 5) reflected over y-axis becomes?
(0, 5)
Reflect (−5, 4) over y-axis, then x-axis.
(5, −4)
Reflect (2, −4) over x = 0 (y-axis)
(−2, −4)
A student says reflection over x-axis changes x-values. Correct?
No, it changes y-values
Triangle A(1,2), B(3,4), C(5,1) is reflected over x-axis. New coordinates?
A′(1,−2), B′(3,−4), C′(5,−1)
Reflect triangle A(2,1), B(4,3), C(6,2) over y-axis.
A′(−2,1), B′(−4,3), C′(−6,2)
Start at (3, −6). Reflect over x-axis then y-axis.
(−3, 6)
A point is reflected over the x-axis and then over the y-axis. It ends at (−6, 2). What was the original point?
(6, −2)
What transformation is a reflection over y = x?
Swap coordinates (x, y → y, x)