Unit 1, Lesson 4
Coordinate Moves
Accelerated 7
4.1
Warm-up
Select all of the translations that take Triangle T to Triangle U. There may be more than one correct answer.
A. Translate to .
B. Translate to .
C. Translate to .
D. Translate to .
4.2
Activity
- Here is a list of points:
, , , ,
On the coordinate plane:- Plot each point and label each with its coordinates.
- Using the -axis as the line of reflection, plot the image of each point.
- Label the image of each point with its coordinates.
- Include a label using a letter. For example, the image of point should be labeled .
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If the point were reflected using the -axis as the line of reflection, what would be the coordinates of the image? What about ? ? Explain how you know.
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The point has coordinates .
- Without graphing, predict the coordinates of the image of point if point were reflected using the -axis as the line of reflection.
- Check your answer by finding the image of on the graph.
- Label the image of point as .
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What are the coordinates of ?
- Suppose you reflect a point using the -axis as the line of reflection. How would you describe its image?
4.3
Activity
Apply each of the following transformations to segment .
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Rotate segment counterclockwise around center . Label the image of as . What are the coordinates of ?
- Rotate segment counterclockwise around center . Label the image of as . What are the coordinates of ?
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Rotate segment clockwise around . Label the image of as and the image of as . What are the coordinates of and ?
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Compare the two counterclockwise rotations of segment . What is the same about the images of these rotations? What is different?
Student Lesson Summary
We can use coordinates to describe points and find patterns in the coordinates of transformed points.
We can describe a translation by expressing it as a sequence of horizontal and vertical translations.
For example, segment is translated right 3 and down 2.
Quadrilateral on a coordinate plane. Horizontal axis scale negative 3 to 5 by 1’s. Vertical axis scale negative 2 to 3 by 1’s. Quadrilateral A B B prime A prime has coordinates A(negative 2 comma 1), B(1 comma 2), B prime(4 comma 0) and A prime (1 comma negative 1).
Reflecting a point across an axis changes the sign of one coordinate.
For example, reflecting the point whose coordinates are across the -axis changes the sign of the -coordinate, making its image the point whose coordinates are . Reflecting the point across the -axis changes the sign of the -coordinate, making the image the point whose coordinates are .
3 points on a coordinate plane. Horizontal axis scale negative 3 to 5 by 1’s. Vertical axis scale negative 2 to 2 by 1’s. The points have these coordinates: A(2 comma negative 1), A prime(2 comma 1) and A double prime (negative 2 comma negative 1).
Reflections across other lines are more complex to describe.
We don’t have the tools yet to describe rotations in terms of coordinates in general. Here is an example of a rotation with center in a counterclockwise direction.
Point has coordinates . Segment is rotated counterclockwise around . Point with coordinates rotates to point whose coordinates are .
Segment A B rotated on a coordinate plane, origin O. Horizontal axis scale negative 4 to 4 by 1’s. Vertical axis scale negative 2 to 4 by 1’s. The segments have these coordinates: A(0 comma 0), B(2 comma 3) and B prime (negative 3 comma 2). Angle B A B prime is a right angle.
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