Page 75 - Math Course 2 (Book 2)

Transformations: Reflected Images

Reflection on a Coordinate Plane
Let’s Begin
Example

Reflecting a Figure in a Line COORDINATE GEOMETRY

Quadrilateral ABCD has vertices A(1, 1), B(3, 2),
Example C(4, –1), and D(2, –3). Graph ABCD and its
image under reflection in the x-axis. Compare
the coordinates of each vertex with the
Draw the reflected image of quadrilateral WXYZ in coordinates of its image.
line p. Use the vertical grid lines to find the corresponding
point for each vertex so that the x-axis is equidistant
from each vertex and its image.
Step 1
Draw segments perpendicular to line p from each
point W, X, Y, and Z. A(1, 1) → A’ (1, –1)

Step 2 B(3, 2) → B’ (3, –2)
Locate W’, X’, Y’, and Z’ so that line p is the
perpendicular bisector of WW’, XX’, YY’ and ZZ’, C(4, –1) → C’ (4, 1)
Points W’, X’, Y’, and Z’ are the respective images
of W, X, Y, and Z. D(2, –3) → D’ (2, 3)

Y
Plot the reflected vertices and connect to form the
image A’B’C’D’.
W X

W’

Y’ X’ Z

Z’

Step 3
Connect vertices W’, X’, Y’, and Z’.

Since points W', X', Y', and Z' are
the images of points W, X, Y, The x-coordinates stay the same,
and Z under reflection in line p, but the y-coordinates are
Answer Answer
then quadrilateral W'X'Y'Z' is the opposite. That is, (a, b) → (a, –b).
reflection of quadrilateral WXYZ
in line p.

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