High School
1.)A pentagon is translated down and to the left. How many sides does the resulting figure have?
a)6
b)5
c)4
d)It is impossible to determine without knowing how far the pentagon was translated.
3.)Which of the following capital letters results in the same letter over again when reflected about a horizontal line?
a)D
b)S
c)Y
d)A
4.) A quadrilateral has vertices A, B, C, and D. A line of reflection is drawn so that A is 6 units away from the line, B is 4 units away from the line, C is 7 units away from the line, and D is 9 units away from the line. When quadrilateral ABCD is reflected about the line of reflection to create a new quadrilateral A′B′C′D′, which resulting point is closest to the line of reflection?
a)D′
b)B′
c)A′
d)C′
5.) A pre-image arrow pointing east is rotated 135° clockwise. In which direction is the image arrow pointing?
a)southwest
b)west
c)northwest
d)southeast
6.) A point is rotated 272° clockwise. What is the equivalent smallest positive counterclockwise rotation?
written answer
9.)A rotation by how many degrees represents six full rotations?
written answer
10.)What is true about the number of sides in any regular polygon that has at least one line of symmetry passing through two vertices?
a)The number of sides is prime.
b)The number of sides is odd.
c)The number of sides is a perfect square.
d)The number of sides is even.
14.)
15.)Which of the following series of transformations is equivalent to reflecting about the line y=−x?
a)reflecting about the y-axis and then rotating 90° counterclockwise
b)reflecting about the x-axis and then rotating 180° counterclockwise
c)reflecting about the y-axis and then rotating 180° counterclockwise
d)reflecting about the x-axis and then rotating 90° counterclockwise
16.)Which point maps to itself both when reflected about y=x and reflected about y=−x?
a)(−1,1)
b)(0,0)
c)(1,1)
d)(0,1)
17.)True or false: Sequences of rigid motions can be applied to any type of polygon.
a)This statement is false. Sequences of rigid motions can only be applied to polygons with fewer than 10 vertices.
b)This statement is false. Sequences of rigid motions can only be applied to convex polygons.
c)This statement is true.
d)This statement is false. No more than one rigid motion can be applied to any polygon.
18.) True or false: A sequence of rigid motions that maps a pre-image to an image must contain no fewer than two unique rigid motions for the pre-image and the image to be congruent.
a) This statement is false. If a sequence of rigid motions maps a pre-image to an image, the pre-image and the image are congruent no matter the details of the sequence of rigid motions.
b)This statement is true.
c) This statement is false. A sequence of rigid motions that maps a pre-image to an image must contain no more than two unique rigid motions for the pre-image and the image to be congruent.
d) This statement is false. A sequence of rigid motions that maps a pre-image to an image must contain exactly two unique rigid motions for the pre-image and the image to be congruent.
can you just help? sheesh some of us don't wanna spend 100 years learning about something they'll never need to know.
does anyone have the answer
1.) To determine the number of sides the resulting figure has after a translation, we first need to understand what a translation is. In a translation, a shape is moved in a specific direction, either up/down or left/right, without any rotation or resizing. The translated figure will have the same shape as the original, just in a different position.
In this case, the pentagon is translated down and to the left. Since a translation does not affect the number of sides, the resulting figure will still have 5 sides, just positioned differently. Therefore, the answer is (b) 5.
3.) To determine which capital letter results in the same letter over again when reflected about a horizontal line, we can visualize the letters and their mirror images.
When the letter D is reflected about a horizontal line, it becomes a different letter (b).
When the letter S is reflected about a horizontal line, it becomes a different letter (Z).
When the letter Y is reflected about a horizontal line, it remains the same letter (Y).
When the letter A is reflected about a horizontal line, it becomes a different letter (V).
Therefore, the answer is (c) Y.
4.) To determine which resulting point is closest to the line of reflection after reflecting quadrilateral ABCD, we need to analyze the distances of each vertex from the line of reflection.
Given the distances:
A is 6 units away from the line,
B is 4 units away from the line,
C is 7 units away from the line,
and D is 9 units away from the line.
When reflecting over a line, the distance from a point to the line remains the same after reflection.
Therefore, the resulting point that is closest to the line of reflection is B′, which is 4 units away. The answer is (b) B′.
5.) To determine the direction in which the image arrow is pointing after rotating a pre-image arrow 135° clockwise, we need to visualize the rotation.
Start with the pre-image arrow pointing east. Clockwise rotation means that we rotate in the direction opposite to how the hands of a clock move. 135° clockwise is equivalent to a quarter rotation clockwise.
After rotating the pre-image arrow 135° clockwise, the image arrow will be pointing in the southwest direction. Therefore, the answer is (a) southwest.
6.) To find the equivalent smallest positive counterclockwise rotation for a given clockwise rotation, we need to understand that a full rotation is 360°.
Given a rotation of 272° clockwise, we can find the equivalent counterclockwise rotation by subtracting this angle from a full rotation (360°).
360° - 272° = 88°
Therefore, the equivalent smallest positive counterclockwise rotation is 88°.
9.) To determine the rotation angle that represents six full rotations, we need to understand that a full rotation is 360°.
To find the angle representing six full rotations, we multiply 360° by six.
360° * 6 = 2160°
Therefore, 2160° represents six full rotations.
10.) To determine the number of sides in a regular polygon that has at least one line of symmetry passing through two vertices, we need to understand what line(s) of symmetry means for a polygon.
A line of symmetry is a line that divides a shape into two congruent halves, such that if the shape is folded along that line, the two halves will perfectly overlap.
For a regular polygon, if it has at least one line of symmetry passing through two vertices, it means that the polygon is symmetrical and has rotational symmetry.
In a polygon with rotational symmetry, the number of sides is an even number. This is because for each side, there is a corresponding side on the opposite side of the line of symmetry. Therefore, the answer is (d) the number of sides is even.
15.) To determine which series of transformations is equivalent to reflecting about the line y = -x, we need to understand what each transformation does.
Reflecting about the y-axis means flipping an object horizontally.
Rotating counterclockwise means turning the object to the left.
Now, let's analyze the options:
a) Reflecting about the y-axis and then rotating 90° counterclockwise:
This combination of transformations does not match the reflection about the line y = -x.
b) Reflecting about the x-axis and then rotating 180° counterclockwise:
This combination of transformations does not match the reflection about the line y = -x.
c) Reflecting about the y-axis and then rotating 180° counterclockwise:
This combination of transformations matches the reflection about the line y = -x, as reflecting about the y-axis corresponds to flipping the shape horizontally, and then rotating 180° counterclockwise corresponds to turning the shape to the left.
d) Reflecting about the x-axis and then rotating 90° counterclockwise:
This combination of transformations does not match the reflection about the line y = -x.
Therefore, the answer is (c) reflecting about the y-axis and then rotating 180° counterclockwise.
16.) To determine which point maps to itself when reflected about y = x and y = -x, we need to visualize the reflection.
The line y = x is a diagonal line that passes through the origin (0,0) and has a slope of 1.
The line y = -x is also a diagonal line that passes through the origin (0,0) but has a slope of -1.
Let's analyze the points:
a) (-1,1)
When reflected about y = x, this point maps to the point (1,-1). However, when reflected about y = -x, this point does not map to itself.
b) (0,0)
When reflected about y = x, this point remains the same. When reflected about y = -x, this point remains the same.
Therefore, (0,0) maps to itself both when reflected about y = x and y = -x.
c) (1,1)
When reflected about y = x, this point maps to itself. But when reflected about y = -x, this point does not map to itself.
d) (0,1)
When reflected about y = x, this point maps to itself. But when reflected about y = -x, this point does not map to itself.
Therefore, the answer is (b) (0,0).
17.) To determine whether sequences of rigid motions can be applied to any type of polygon, we need to understand what rigid motions are and their limitations.
Rigid motions in geometry include translations, rotations, and reflections. These motions preserve distance, angle measures, and shape. They do not change the size or shape of the original object.
The statement "Sequences of rigid motions can be applied to any type of polygon" is true. Sequences of rigid motions can be applied to any polygon, regardless of the number of vertices or whether the polygon is convex or concave. Rigid motions can be used to transform one polygon into another, preserving its shape and size.
Therefore, the answer is (c) This statement is true.
18.) To determine whether a sequence of rigid motions that maps a pre-image to an image must contain no fewer than two unique rigid motions for the pre-image and image to be congruent, we need to understand the concept of congruence.
Congruent shapes are identical in shape and size. A sequence of rigid motions can be used to transform a pre-image into an image, and if the pre-image and image overlap perfectly, they are congruent.
The statement "A sequence of rigid motions that maps a pre-image to an image must contain no fewer than two unique rigid motions for the pre-image and image to be congruent" is false. As long as the sequence of rigid motions transforms the pre-image into the image such that they overlap perfectly, they are congruent. The number of unique rigid motions used in the sequence does not determine congruence.
Therefore, the answer is (a) This statement is false. If a sequence of rigid motions maps a pre-image to an image, the pre-image and the image are congruent no matter the details of the sequence of rigid motions.
so no one gon answer?
We do not do your homework for you. Although it might take more effort to do the work on your own, you will profit more from your effort. We will be happy to evaluate your work though.
What are your choices?