Lesson Plan-Grade 9
Lesson Title: Reflections
State Standards: MA.912.G.2.6
Use coordinate geometry to prove properties of congruent, regular and
similar polygons, and to perform transformations in the plane.
Grade : 9 (FCAT)
Subject: Mathematics
Objectives:
The students will identify and
locate reflections
Lesson Procedure and
Evaluation:
Recapitulation (10 mins):
Student will be able to recall that a reflection
can be seen in water, in a mirror, or in a shiny surface. An object and its reflection have the same
shape and size, but the figures face in opposite directions. Student will be
also able to recall the concepts of congruency and similarity of geometrical
shapes
Explanation: (40 mins)
Activity 1:
Reflections in the Coordinate Plane:
Reflecting over the x-axis: (the x-axis as the line of reflection)
The
reflection of the point (x, y) across the x-axis is the point (x, -y).
Reflecting over the y-axis: (the y-axis
as the line of reflection)
The
reflection of the point (x,
y) across the y-axis
is the point (-x, y).
Reflecting over the line y = x or y = -x:
(the lines y = x or y = -x as the lines of reflection)
The
reflection of the point (x,
y) across the line y = x is the point (y, x).
The
reflection of the point (x,
y) across the line y = -x is the point (-y, -x).
Activity 2:
Reflecting over any
line:
Each
point of a reflected image is the same distance from the line of reflection as
the corresponding point of the original figure.
In other words, the line of reflection lies directly in the middle
between the figure and its image -- it is the perpendicular bisector of the
segment joining any point to its image.
Keep this idea in mind when working with lines of reflections that are
neither the x-axis nor the y-axis.
Recapitulation and Evaluation: (10 mins)
- Find the image of the point
(4,-3) under a reflection across the x-axis.
- Find the image of the point (-5,-7)
under a reflection across the y-axis.
