Reflecting Points and Graphs

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Reflecting Points and Graphs
Created by Kenny Kong HKIS 200
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Reflecting Points and Graphs

• A transformation that flips a figure to generate
  a mirror image is called a reflection.

• A point is reflected across the y-axis when you
  change the sign of its x-coordinate.

i.e. (x, y) ? (-x, y)

• A point is reflected across the x-axis when you
  change the sign of its y-coordinate.

i.e. (x, y) ? (x, -y)
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Reflection across the x-axis

• A point is reflected across the x-axis when you
  change the sign of its y-coordinate.

All the coordinate points are changed in the form
of (x, -y).
Reflected across the x-axis, point B (5,2) has
been changed to point B
All the signs of the y-coordinate are changed to
their opposite.
Original Figure
C
(5, -2).
A
B
Reflected across the x-axis, point A (3,2) has
been changed to point A
Reflected across the x-axis, point C (3,5) has
been changed to point C
A
B
C
(3, -2).
(3, -5).
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Reflection across the y-axis

• A point is reflected across the y-axis when you
  change the sign of its x-coordinate.

All the coordinate points are changed in the form
of (- x, y).
Reflected across the y-axis, point B (5,2) has
been changed to point B
Original Figure
C
C
A
A
B
(-5, 2).
B
Reflected across the y-axis, point A (3,2) has
been changed to point A
Reflected across the y-axis, point C (3,5) has
been changed to point C
All the signs of the x-coordinate are changed to
their opposite.
(-3, 2).
(-3, 5).
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Reflection across the x-axis

• A point is reflected across the x-axis when you
  change the sign of its y-coordinate.

All the coordinate points are changed in the form
of (x, -y).
Reflected across the x-axis, point B (3,6) has
been changed to point B
B
(3, -6).
A
?The new function is
All the signs of the y-coordinate are
changed to their opposite.
Reflected across the x-axis, point A (1,2) has
been changed to point A
A
y -((x)2 2)
y -(x)2 ? 2
B
(1, -2).
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Reflection across the x-axis

• A point is reflected across the x-axis when you
  change the sign of its y-coordinate.

All the coordinate points are changed in the form
of (x, -y).
Reflected across the x-axis, point B (3,6) has
been changed to point B
B
A
(3, -6).
All the signs of the y-coordinate are changed to
their opposite.
?The new function is
Reflected across the x-axis, point A (1,2) has
been changed to point A
A
y -((x ? 1)2 2)
y -(x ? 1)2 ? 2
B
(1, -2).
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Reflection across the y-axis

• A point is reflected across the y-axis when you
  change the sign of its x-coordinate.

All the coordinate points are changed in the form
of (- x, y).
Reflected across the y-axis, point B (3,6) has
been changed to point B
B
B
(-3, 6).
A
A
?The new function is
Reflected across the y-axis, point A (1,2) has
been changed to point A
y (-x ? 1)2 2
All the signs of the x-coordinate are changed to
their opposite.
(-1, 2).
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Reflection across the x-axis

• A point is reflected across the x-axis when you
  change the sign of its y-coordinate.

All the coordinate points are changed in the form
of (x, -y).
Reflected across the x-axis, point B (5,6) has
been changed to point B
B
All the signs of the y-coordinate are changed to
their opposite.
(5, -6).
A
?The new function is
Reflected across the x-axis, point A (1,2) has
been changed to point A
A
y -(? x ? 1)
y -? x ? ? 1
B
(1, -2).
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Tips

• The negative sign added just in front of the x in
  any functions suggests a flip over the y-axis.

E.g. y x 1 ? y -x 1
y ?x? 2 ? y ?-x? 2
y x2 3 ? y (-x)2 3
y 2x 4 ? y 2-x 4

• The negative sign distributed to all the terms on
  the x side of functions suggests a flip over the
  x-axis.

E.g. y x 1 ? y -(x 1) -x ? 1
y ?x? 2 ? y -(?x? 2) -?x? ? 2
y x2 3 ? y -((x)2 3) -(x)2 ? 3
y 2x 4 ? y -(2x 4) -2x ? 4