Unit 1, Lesson 7
Rotation Patterns
Accelerated 7
7.1
Warm-up
What do you notice? What do you wonder?
7.2
Activity
<p>Point <span class="math" data-png-file-id="51">\(E\)</span> and line segment <span class="math" data-png-file-id="11027">\(\overline{C\ D }\)</span> with midpoint <span class="math" data-png-file-id="27">\(G\)</span>. Let (0 comma 0) be the bottom left corner of the grid. Then the coordinates of line segment <span class="math" data-png-file-id="11021">\(\overline{ C\ D }\)</span> are: <span class="math" data-png-file-id="7">\(C\)</span>(2 comma 2), <span class="math" data-png-file-id="27">\(G\)</span>(4 comma 3) and <span class="math" data-png-file-id="12">\(D\)</span>(6 comma 4). The coordinates of point <span class="math" data-png-file-id="51">\(E\)</span> are <span class="math" data-png-file-id="51">\(E\)</span>(5 comma 5).</p>
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Rotate segment around point . Draw its image and label the image of as
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Rotate segment around point . Draw its image and label the image of as and the image of as .
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Rotate segment around its midpoint, What is the image of ?
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What happens when you rotate a segment around a point?
Student Lesson Summary
When we apply a 180-degree rotation to a line segment, there are several possible outcomes:
- The image of the segment maps is the same as the original (if the center of rotation is the midpoint of the segment).
- The image of the segment overlaps with the segment and lies on the same line (if the center of rotation is a point on the segment).
- The image of the segment does not overlap with the segment and is parallel to the original segment (if the center of rotation is not on the segment).
This can also tell us important information about a figure that has been rotated. In this example, triangle has been rotated 180 degrees with point as the center of rotation. If we think of side as a line segment, then we know that its image must be parallel to it. If we think of side as a line segment, then we know that its image must be along the same line.
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