Definition: A rigid transformation (also called an isometry) is a transformation of the plane that preserves length.
Four types of isometries:
1. Translation -- sliding a shape from one spot to another on the xy-plane;
2. Reflection -- creating a mirror image of a shape by reflecting a shape over a line, called the axis of reflection, on the xy-plane;
3. Rotation -- rotating a shape around a point, called the center of rotation, on the xy-plane;
4. Glide reflection -- a composite transformation which is a translation followed by a reflection in line parallel to the direction of translation.
Translations, reflections, and rotations don't change the shape or size of the shape being transformed, so we can see that these three types of transformations are isometric, the glide reflection doesn't change the shape or size of the shape being transformed, but changes orientation.
A composition or sequence of isometries occurs when two or more transformations are combined to form a new transformation. In a composition, one transformation produces an image upon which the other transformation is then performed (as for the glide reflection). The composition of isometries is always the isometry (preserves lengths).
Answer: correct choice is B.
Answer:
940800 different ways to create the committee.
Step-by-step explanation:
1 chosen from 100 leaves 98 to chose from on the second pick because the other senator from the same state is also eliminated. The second choice leaves 96 available for the third selection.
So multiply 100×98×96=940800
Answer:
He needs at least 77 on the 5th test.
<em>T₅ ≥ 77</em>
Step-by-step explanation:
If five numbers are to average 84, then their sum must be (5 x 84) = 420 .
Gale needs his five grades to add up to 420.
So far, he has (80 + 95 + 78 + 90) = 343 .
He needs at least (420 - 343) = <em>77 more</em> points on the 5th test.
Answer:
A
Step-by-step explanation:
The package with the most low cost is 7.
