What type of polygon would a slice of a hexahedron at a vertex create? Explain. What type of polygon would a slice of an icosahe
dron at a vertex create? Explain.
1 answer:
Answer:
- hexahedron: triangle or quadrilateral or pentagon
- icosahedron: quadrilateral or pentagon
Step-by-step explanation:
<u>Hexahedron</u>
A hexahedron has 6 faces. A <em>regular</em> hexahedron is a cube. 3 square faces meet at each vertex.
If the hexahedron is not regular, depending on how those faces are arranged, a slice near a vertex may intersect 3, 4, or 5 faces. The first attachment shows 3- and 4-edges meeting at a vertex. If those two vertices were merged, then there would be 5 edges meeting at the vertex of the resulting pentagonal pyramid.
A slice near a vertex may create a triangle, quadrilateral, or pentagon.
<u>Icosahedron</u>
An icosahedron has 20 faces. The faces of a <em>regular</em> icosahedron are all equilateral triangles. 5 triangles meet at each vertex.
If the icosahedron is not regular, depending on how the faces are arranged, a slice near the vertex may intersect from 3 to 19 faces.
A slice near a vertex may create a polygon of 3 to 19 sides..
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Given:
Vertices of triangle ABC are A (1,4), B(3,−2) and C(4,2).
Triangle ABC reflected over the x-axis to get the triangle A'B'C'.
To find:
The coordinates of the image A'B'C'.
Solution:
If a figure reflected over the x-axis, then rule of transformation is
Now, using this rule, we get
Therefore, the coordinates of the image A'B'C' after a reflection over the x-axis are A'(1,-4), B'(3,2) and C'(4,-2).