6.3 Line Reflections in the Coordinate Plane
Reflect a pt over the x‐axis
Reflect a pt over the y‐axis
rx‐axis(A) = A'
ry‐axis(A) = A'
RULE ‐ Reflection in the y‐axis: ry‐axis(x,y) ‐‐‐> (‐x,y) ....negate x,y stays the same
original pt
RULE ‐ Reflection in the x‐axis: rx‐axis(x,y) ‐‐‐> (x,‐y) ....negate y,x stays the same
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EXAMPLES
rx‐axis(3,4) =
ry‐axis(2,5) =
ry‐axis(‐1,0) =
rx‐axis(0,5) =
rx‐axis(5,0) =
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Reflecting over other horizontal or vertical lines:
1. What is the equation of line l?
2. What is the equation of line k?
3. What is the equation of the x‐axis?
4. What is the equation of the y‐axis?
5. rl(A) = 6. rk (A')
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ry=5 (1,2) = 4
Reflect a pt over y=x
*y=x is the equation of a line
Reflect a pt over the y= ‐x
*y=‐x is the equation of a line
RULE ‐ ry=x(x,y) ‐‐‐> (y,x) ....switch coordinates
RULE ‐ ry=‐x(x,y) ‐‐‐> (‐y,‐x) ....switch and negate
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6.4 Point Reflections in the Coordinate Plane
A reflection over a fixed point ‐ use the concept of slope (rise and run)
Symbol: R (capital R)
R (A) =
nothing below so assume the origin
RO(‐2,3)
R(0,0)(‐2,3)
*the reflected pt should be collinear with the original pt ant the pt of reflection is the midpt of the segment
Point Reflection in the origin: RO(x,y) ‐‐‐> (‐x,‐y)...negate both
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Properties:
1. Distance stays the same
2. Angle measures stay the same
3. Points in a line, stay in a line
4. Midpoints stay the same
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HOMEWORK: pg 226 #3‐17,21 AND pg 231 #3‐8,15,16
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