Name ___________________________
Reflections in the Coordinate Plane
In this activity, you’ll investigate what happens to the coordinates of points when
you reflect them across the x- and y-axis in the coordinate plane.
1.
Chose Show Grid from the Graph menu.
2.
Draw triangle CDE in the first quadrant with vertices on the grid. In order
to do this, chose Snap Points from the Graph menu.
3.
Measure the coordinates of each vertex.
4.
Mark the y-axis as a mirror.
5.
Reflect the triangle across the y-axis by selecting the whole triangle and
choosing Reflect from the Transform menu. Your sketch should know
look like the following:
C: (1.01, 1.01)
D
D'
4
D: (2.99, 4.00)
E: (5.00, 2.01)
E'
2
E
C
C'
-5
5
-2
-4
-6
6.
Measure the coordinates of the image’s vertices.
7.
Drag the vertices to different points on the grid and look for a relationship
between a point’s coordinates and the coordinates of the reflected image
across the y-axis.
Question 1: Describe any relationship you observe between the coordinates of
the vertices of your original triangle and the coordinates of their
reflected images across the y-axis.
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8.
Now mark the x-axis as a mirror and reflect your original triangle across
the x-axis.
9.
Before you measure the coordinates of this image, predict what they will
be. Then measure to confirm your prediction.
Prediction: _____________________________________________________
Question 2: Describe any relationship you observe between the coordinates of
the vertices of your original triangle and the coordinates of their
reflected images across the x-axis.
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10.
Start a new sketch and redo steps 1-3.
11.
Draw the line y=x on the grid. Try to do this on your own. Write down the
steps that you tried. If you must, read the hint at the bottom of the last
page. However, you must TRY something in order to read the hint.
Write the steps that you tried below. Check with me when you are finished.
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12.
Mark the line y=x as a mirror.
13.
Reflect the triangle across the line y=x by selecting the whole triangle and
choosing Reflect from the Transform menu.
14.
Before you measure the coordinates of this image, predict what they will
be. Then measure to confirm your prediction.
Prediction: _____________________________________________________
Question 3: Describe any relationship you observe between the coordinates of
the vertices of your original triangle and the coordinates of their
reflected images across the line y = x.
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Summary:
Use the following chart to summarize your results:
Original Triangle
(x, y)
Triangle
Reflected across
the x-axis
Triangle
Reflected across
the y-axis
Triangle
Reflected across
the line y=x
Hint: Use your point tool to create a point at (1, 1). Then select this point and
the origin and choose Line from the construct menu.
Name ___________________________
Translations in the Coordinate Plane
In this activity, you’ll investigate what happens to the coordinates of points when
they are translated in the coordinate plane.
1.
Chose Show Grid from the Graph menu.
2.
Chose Snap Points from the Graph menu.
3.
Draw a segment from the origin to anywhere on the grid. Label the
endpoint C.
3.
Measure the coordinates of point C only.
4.
Mark the vector that you just constructed. TO do this, chose both ends of
the vector and chose Mark Vector from the Transform menu.
5.
Draw triangle DEF with vertices on the grid in the first quadrant. Measure
the vertices.
6.
Translate the triangle by the marked vector. (Select the triangle and
choose Translate under the construct menu. Make sure Marked is
selected).
7.
Measure the coordinates of the image’s vertices.
8.
Experiment by dragging point C or any of the triangles vertices. Look for a
relationship between a point’s coordinates and the coordinates of its
image under a translation.
Question 1: Where can you drag point C so that the original points and the
corresponding image points always have the same y-coordinates
but different x-coordinates?
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Question 2: Where can you drag point C so that the original point and the
corresponding image points always have the same x-coordinates
but different y-coordinates?
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Question 3: When the vector defined by the origin and point C translates your
original triangle to the left and up, what must be true of the
coordinates of point C?
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Question 4: Move the endpoint, C, of the vector to point (2, 1). How are the
point D and D' related? How are the point E and E' related? How
are the point F and F' related?
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Question 5: Move the endpoint, C, of the vector to point (1, 3). How are the
point D and D' related? How are the point E and E' related? How
are the point F and F' related?
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Question 6: Summary Statement- Suppose point C has coordinates (x, y).
What are the coordinates of the image of a point under translation
by (a, b)?
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Name ___________________________
Rotations in the Coordinate Plane
In this activity, you will investigate what happens to the coordinates of points
when they are rotated in the coordinate plane about the origin.
1.
Show the grid.
2.
Mark the origin as a center of rotation by selecting the origin and choosing
Mark Center from the transform menu.
3.
Draw triangle CDE with vertices on the grid in the first quadrant. In order
to do this, chose Snap Points from the Graph menu.
4.
Measure the coordinates of each vertex.
5.
Select the triangle and rotate it 90°. Measure the coordinates of the
image.
Question 1: Describe any relationship you observe between the coordinates of
the vertices of your original triangle and the coordinates of the
images rotated 90° about the origin.
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6.
Rotate the original triangle 180° about the origin.
7.
Before you measure the coordinates of this image, predict what they will
be. Then measure to confirm your prediction.
Prediction: _____________________________________________________
Question 2: Describe any relationship you observe between the coordinates of
the vertices of your original triangle and the coordinates of the
images rotated 180° about the origin.
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8.
Rotate the original triangle 270° about the origin.
9.
Before you measure the coordinates of this image, predict what they will
be. Then measure to confirm your prediction.
Prediction: _____________________________________________________
Question 3: Describe any relationship you observe between the coordinates of
the vertices of your original triangle and the coordinates of the
images rotated 270° about the origin.
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Question 4: If you rotate the original triangle 360º about the origin, where will it
end up? How do you know?
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Summary:
Use the following chart to summarize your results:
Original Triangle
Triangle Rotated
90º about origin
Triangle Rotated
180º about origin
Triangle Rotated
270º about origin
(x, y)