Text of 9-1 Reflections You identified reflections. Draw reflections. Draw reflections in the coordinate...
Slide 1
9-1 Reflections You identified reflections. Draw reflections.
Draw reflections in the coordinate plane.
Slide 2
Reflection She saw her reflection in the mirror. The trees were
reflected in the lake. The sphere was so clear, I saw my
reflection.
Slide 3
Definition of Reflection A reflection is a flipping of a figure
over a line. This is the line of reflection. A reflection is a
special type of transformation. Line of Reflection
Slide 4
Pre-Image/Image Pre-imagethe original figure Imagethe figure
after a transformation A C BAABB CC l Pre-image (1)Image (2)
Slide 5
Pre-image/Image To tell the two images apart, use prime
notation A. When naming images of figures, list corresponding
points in the same order.
Slide 6
Reflective Detective Fold a sheet of paper in half. Poke the
tip of a pencil through the folded paper at 3 points that are not
collinear. Open the paper and draw segments connecting the holes on
each side of the fold. (You should have 2 triangles with the fold
as the line of reflection.) Label all the points. Draw segments
connecting the points of the image with corresponding points of the
pre-image. Measure the distance from the vertices to the fold.
Measure the angles these segments make with the fold.
Slide 7
Vocabulary Equidistanttwo points are the same distance from
another point, segment or line. Bisectora figure is cut into two
congruent halves. Perpendicular bisectora line or segment that
divides the segment into two congruent segments and is
perpendicular to it. A l B l is a perpendicular bisector of AB
Slide 8
p. 623
Slide 9
Draw the reflected image of quadrilateral WXYZ in line p. Step
1 Draw segments perpendicular to line p from each point W, X, Y,
and Z. Step 2 Locate W', X', Y', and Z' so that line p is the
perpendicular bisector of Points W', X', Y', and Z' are the
respective images of W, X, Y, and Z. Reflect a Figure in a
Line
Slide 10
Step 3 Connect vertices W', X', Y', and Z'. Answer: Since
points W', X', Y', and Z' are the images of points W, X, Y, and Z
under reflection in line p, then quadrilateral W'X'Y'Z' is the
reflection of quadrilateral WXYZ in line p.
Slide 11
Draw the reflected image of quadrilateral ABCD in line n. A.B.
C.D.
Slide 12
Reflect a Figure in a Horizontal or Vertical Line A.
Quadrilateral JKLM has vertices J(2, 3), K(3, 2), L(2, 1), and M(0,
1). Graph JKLM and its image over x = 1.
Slide 13
Use the horizontal grid lines to find a corresponding point for
each vertex so that each vertex and its image are equidistant from
the line x = 1. Answer:
Slide 14
Reflect a Figure in a Horizontal or Vertical Line Use the
horizontal grid lines to find a corresponding point for each vertex
so that each vertex and its image are equidistant from the line x =
1. Answer:
Slide 15
Reflect a Figure in a Horizontal or Vertical Line B.
Quadrilateral JKLM has vertices J(2, 3), K(3, 2), L(2, 1), and M(0,
1). Graph JKLM and its image over y = 2.
Slide 16
Use the vertical grid lines to find a corresponding point for
each vertex so that each vertex and its image are equidistant from
the line y = 2. Answer:
Slide 17
A. Quadrilateral ABCD has vertices A(1, 2), B(0, 1), C(1, 2),
and D(3, 0). Graph ABCD and its image over x = 2. A.B. C.D.
Slide 18
p. 625
Slide 19
A. Graph quadrilateral ABCD with vertices A(1, 1), B(3, 2),
C(4, 1), and D(2, 3) and its image reflected in the x-axis.
Multiply the y-coordinate of each vertex by 1. (x, y) (x, y) A(1,
1) A'(1, 1) B(3, 2) B'(3, 2) C(4, 1) C'(4, 1) D(2, 3) D'(2, 3)
Answer: Reflect a Figure in the x- or y-axis
Slide 20
B. Graph quadrilateral ABCD with vertices A(1, 1), B(3, 2),
C(4, 1), and D(2, 3) and its reflected image in the y-axis.
Multiply the x-coordinate of each vertex by 1. (x, y) (x, y) A(1,
1) A'(1, 1) B(3, 2) B'(3, 2) C(4, 1) C'(4, 1) D(2, 3) D'(2, 3)
Answer:
Slide 21
A.L'(3, 1), M'(5, 2), N'(6, 1), O'(4, 3) B.L'(3, 1), M'(5, 2),
N'(6, 1), O'(4, 3) C.L'(3, 1), M'(5, 2), N'(6, 1), O'(4, 3) D.L'(1,
3), M'(2, 5), N'(1, 6), O'(3, 4) A. Graph quadrilateral LMNO with
vertices L(3, 1), M(5, 2), N(6, 1), and O(4, 3) and its reflected
image in the x-axis. Select the correct coordinates for the new
quadrilateral L'M'N'O'.
Slide 22
p. 626
Slide 23
Reflect a Figure in the Line y = x Quadrilateral ABCD with
vertices A(1, 1), B(3, 2), C(4, 1), and D(2, 3). Graph ABCD and its
image under reflection of the line y = x. Interchange the x- and
y-coordinates of each vertex. (x, y) (y, x) A(1, 1) A'(1, 1) B(3,
2) B'(2, 3) C(4, 1) C'(1, 4) D(2, 3) D'(3, 2) Answer: