NAME _____________________________________________ DATE ____________________________ PERIOD _____________
Notes
Reflections
A type of transformation where a figure is flipped over a line of reflection is a reflection. To reflect a figure over the xaxis, multiply the y-coordinates by –1. To reflect a figure over the y-axis, multiply the x-coordinates by –1.
Example
Triangle DEF has vertices D(2, 2), E(5, 4), and F(1, 5). Find the coordinates of the reflected image. Graph the
figure and its reflected image over the x-axis.
Plot the vertices and connect to form ∆DEF. The x-axis is the
line of symmetry. The distance from a point on ∆DEF to the line
of symmetry is the same as the distance from the line of
symmetry to the reflected image. The image coordinates are
D(2, –2), E(5, –4), and F(1, –5).
Exercises
1. Triangle ABC has vertices A(0, 4), B(2, 1), and C(4, 3). Find
the coordinates of the vertices of ABC after a reflection over
the x-axis. Then graph the figure and its reflected image.
For Exercises 2 and 3, use the following information.
Triangle FGH has vertices F(–4, 2), G(2, 2), and H(0, –3).
2. What are the coordinates of the image of point F after a
reflection over the x-axis?
3. Graph triangle FGH and its image after a reflection over the
x-axis.
For Exercises 4–6, use the following information.
Quadrilateral WXYZ has vertices W(3, –1), X(3, –4), Y(0, –1),
and Z(–3, –4).
4. What are the coordinates of the image of point W after a
reflection over the y-axis?
5. What are the coordinates of the image of point X after a
reflection over the y-axis?
6. Graph quadrilateral WXYZ and its image after a reflection
over the y-axis.
Transformations
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NAME _____________________________________________ DATE ____________________________ PERIOD _____________
Homework Practice
Reflections
1. Graph ∆ABC with vertices A(2, 2),
B(5, 4),and C(5, 1) and its reflection
over the x-axis. Then find the
coordinates of the reflected image.
2. Graph square ABCD with vertices
A(–1, 2), B(2, –1), C(5, 2), and D(2, 5)
and its reflection over the y-axis. Then
find the coordinates of the reflected image.
The coordinates of a point and its image after a reflection are given. Describe the reflection as over the x-axis or yaxis.
3. B(1, –2) → Bʹ(1, 2)
4. J(–3, 5) → Jʹ(–3, –5)
5. W(–7, –4) → Wʹ(7, –4)
For Exercises 6–9, use the following information.
Triangle XYZ has vertices X(4, 2), Y(4, 4), and Z(0, 2).
6. What are the coordinates of the image of point X
after a reflection over the y-axis?
7. What are the coordinates of the image of point Y
after a reflection over the y-axis?
8. What are the coordinates of the image of point Z
after a reflection over the y-axis?
9. Graph triangle XYZ and its image after a reflection over the x-axis.
Transformations
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