Which translation rule describes the translation that is 6 units to the right and 5 units down?
(1 point)
Responses
(x, y) → (x + 6, y – 5)
( x, y ) → ( x + 6, y – 5)
(x, y) → (x – 6, y – 5)
( x, y ) → ( x – 6, y – 5)
(x, y) → (x + 6, y + 5)
( x, y ) → ( x + 6, y + 5)
(x, y) → (x – 6, y + 5)
(x, y) → (x + 6, y – 5)
use step by step
To describe a translation that is 6 units to the right and 5 units down, follow these steps:
1. Start with the original point (x, y).
2. Move the x-coordinate 6 units to the right by adding 6 to x: x + 6.
3. Move the y-coordinate 5 units down by subtracting 5 from y: y - 5.
4. Write the translation rule in the form (x, y) → (x + 6, y - 5).
Therefore, the correct translation rule is (x, y) → (x + 6, y - 5).
If point P left parenthesis 4 comma 11 right parenthesis is reflected across the line y = 3, what are the coordinates of its reflection image?
(1 point)
Responses
left parenthesis 2 comma 11 right parenthesis
Image with alt text: left parenthesis 2 comma 11 right parenthesis
left parenthesis 11 comma 4 right parenthesis
Image with alt text: left parenthesis 11 comma 4 right parenthesis
left parenthesis 4 comma negative 11 right parenthesis
Image with alt text: left parenthesis 4 comma negative 11 right parenthesis
left parenthesis 4 comma negative 5 right parenthesis
To reflect a point across the line y = 3, we need to keep the x-coordinate the same and change the sign of the y-coordinate.
Given point P (4, 11), when reflected across the line y = 3, the y-coordinate will be negated.
So, the reflected image of point P will have the coordinates:
(4, -11)
Therefore, the correct coordinates of the reflection image are (4, -11).
The vertices of a triangle are P(–4, 1), Q(–2, –8), and R(8, –1). What are the vertices of the image reflected across the x-axis?
(1 point)
Responses
P'(–4, –1), Q'(–2, 8), and R'(8, 1)
P' (–4, –1), Q' (–2, 8), and R' (8, 1)
P'(4, –1), Q'(2, 8), and R'(–8, 1)
P' (4, –1), Q' (2, 8), and R' (–8, 1)
P'(4, 1), Q'(2, –8), and R'(–8, –1)
P' (4, 1), Q' (2, –8), and R' (–8, –1)
P'(–4, 1), Q'(–2, –8), and R'(8, –1)
To reflect a point across the x-axis, we keep the x-coordinate the same and change the sign of the y-coordinate.
Given the vertices of the triangle: P(-4, 1), Q(-2, -8), and R(8, -1), when reflected across the x-axis, the y-coordinate of each vertex will be negated.
So, the coordinates of the reflected vertices will be:
P' (-4, -1), Q' (-2, 8), and R' (8, 1).
Therefore, the correct vertices of the image reflected across the x-axis are P' (-4, -1), Q' (-2, 8), and R' (8, 1).
Which graph shows a triangle and its reflection image across the y-axis?
(1 point)
Responses
Two right triangles are shown on the coordinate plane.The first triangle has vertices at left-parenthesis negative 4 comma 3 right-parenthesis, left-parenthesis negative 4 comma 1 right-parenthesis, and left-parenthesis 0 comma 1 right-parenthesis. The second triangle has vertices at left-parenthesis 4 comma 3 right-parenthesis, left-parenthesis 4 comma 1 right-parenthesis, and left-parenthesis 0 comma 1 right-parenthesis.
Image with alt text: Two right triangles are shown on the coordinate plane. The first triangle has vertices at left-parenthesis negative 4 comma 3 right-parenthesis, left-parenthesis negative 4 comma 1 right-parenthesis, and left-parenthesis 0 comma 1 right-parenthesis. The second triangle has vertices at left-parenthesis 4 comma 3 right-parenthesis, left-parenthesis 4 comma 1 right-parenthesis, and left-parenthesis 0 comma 1 right-parenthesis.
Two right triangles are shown on the coordinate plane.The first triangle has vertices at left-parenthesis negative 5 comma 2 right-parenthesis, left-parenthesis negative 1 comma 2 right-parenthesis, and left-parenthesis negative 1 comma 4 right-parenthesis. The second triangle has vertices at left-parenthesis 0 comma 1 right-parenthesis, left-parenthesis 4 comma 3 right-parenthesis, and left-parenthesis 4 comma 1 right-parenthesis.
Image with alt text: Two right triangles are shown on the coordinate plane. The first triangle has vertices at left-parenthesis negative 5 comma 2 right-parenthesis, left-parenthesis negative 1 comma 2 right-parenthesis, and left-parenthesis negative 1 comma 4 right-parenthesis. The second triangle has vertices at left-parenthesis 0 comma 1 right-parenthesis, left-parenthesis 4 comma 3 right-parenthesis, and left-parenthesis 4 comma 1 right-parenthesis.
Two right triangles are shown on the coordinate plane.The first triangle has vertices at left-parenthesis negative 3 comma 3 right-parenthesis, left-parenthesis negative 1 comma 3 right-parenthesis, and left-parenthesis negative 1 comma negative 1 right-parenthesis. The second triangle has vertices at left-parenthesis 0 comma 1 right-parenthesis, left-parenthesis 4 comma 3 right-parenthesis, and left-parenthesis 4 comma 1 right-parenthesis.
Image with alt text: Two right triangles are shown on the coordinate plane. The first triangle has vertices at left-parenthesis negative 3 comma 3 right-parenthesis, left-parenthesis negative 1 comma 3 right-parenthesis, and left-parenthesis negative 1 comma negative 1 right-parenthesis. The second triangle has vertices at left-parenthesis 0 comma 1 right-parenthesis, left-parenthesis 4 comma 3 right-parenthesis, and left-parenthesis 4 comma 1 right-parenthesis.
Two right triangles are shown on the coordinate plane.The first triangle has vertices at left-parenthesis negative 1 comma 1 right-parenthesis, left-parenthesis 3 comma 3 right-parenthesis, and left-parenthesis 3 comma 1 right-parenthesis. The second triangle has vertices at left-parenthesis negative 1 comma negative 1 right-parenthesis, left-parenthesis 3 comma negative 3 right-parenthesis, and left-parenthesis 3 comma negative 1 right-parenthesis.
Image with alt text: Two right triangles are shown on the coordinate plane. The first triangle has vertices at left-parenthesis negative 1 comma 1 right-parenthesis, left-parenthesis 3 comma 3 right-parenthesis, and left-parenthesis 3 comma 1 right-parenthesis. The second triangle has vertices at left-parenthesis negative 1 comma negative 1 right-parenthesis, left-parenthesis 3 comma negative 3 right-parenthesis, and left-parenthesis 3 comma negative 1 right-parenthesis.
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The correct graph that shows a triangle and its reflection image across the y-axis is:
Two right triangles are shown on the coordinate plane. The first triangle has vertices at (-4, 3), (-4, 1), and (0, 1). The second triangle has vertices at (4, 3), (4, 1), and (0, 1).
Therefore, the correct response is:
Two right triangles are shown on the coordinate plane. The first triangle has vertices at (-4, 3), (-4, 1), and (0, 1). The second triangle has vertices at (4, 3), (4, 1), and (0, 1).
The hexagon GIKMPR is regular. The dashed line segments form 30° angles.
Hexagon GIKMPR is shown.A hexagon is shown. A point in the middle of the hexagon is labeled O. There are points labeled at each vertex and at the midpoints of each side of the hexagon. Starting at the top of the image, the midpoint of the side is labeled F. Moving clockwise, the points are labeled G, H, I, J, K, L, M, N, N, P Q, and R. There are 6 dotted lines drawn through the hexagon and through point O. One connects midpoints F and L. One connects vertices G and M. One connects midpoints H and N. One connects vertices I and P. One connects midpoints J and Q. One connects vertices K and R.
What is the image of ON after a rotation of 180°?
(1 point)
Responses
ON
ON
OH
OH
OJ
OJ
OL
The image of ON after a rotation of 180° is ON itself.
Therefore, the correct response is ON.
Consider square upper A upper B upper C upper D. What is the angle of rotation about the center that maps modifying above upper A upper B with bar to modifying above upper B upper C with bar? Recall that rotations are counterclockwise.
A square has two horizontal sides, two vertical sides, and a dot at its center. The vertex in the upper left is labeled upper A. The vertex in the upper right is labeled upper B. The vertex in the lower right is labeled upper C. The vertex in the lower left is labeled upper D.
(1 point)
Responses
90º
90º
120º
120º
180º
180º
270º
270º
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The angle of rotation about the center that maps upper A upper B to upper B upper C is 90°.
Therefore, the correct response is 90º.
How many lines of symmetry does the figure have?
A pentagon is shown with single congruence marks on each of its sides.
(1 point)
Responses
1
1
5
5
2
2
0
0
A regular pentagon has 5 lines of symmetry.
Therefore, the correct response is 5.
Which letter has rotational symmetry?
(1 point)
Responses
Q
Q
R
R
S
S
T
The letter "S" has rotational symmetry.
Therefore, the correct response is S.
Which image has reflectional, rotational, and point symmetry?
(1 point)
Responses
A quadrilateral is shown. The top and bottom sides are horizontal and of unequal lengths. The other two sides appear to have the same length.
Image with alt text: A quadrilateral is shown. The top and bottom sides are horizontal and of unequal lengths. The other two sides appear to have the same length.
A six-sided polygon is shown. Each side is marked with a single hash mark.
Image with alt text: A six-sided polygon is shown. Each side is marked with a single hash mark.
A triangle is shown. The sides all have different lengths. The angle between the two shortest sides is greater than 90 degrees.
Image with alt text: A triangle is shown. The sides all have different lengths. The angle between the two shortest sides is greater than 90 degrees.
A five-sided polygon is shown.The two sides forming the top of the form a shape like an Upper V. The side at the bottom is horizontal. The side at the left has a top endpoint higher and further left than the bottom end point. The side at the right has a top endpoint higher and further right than the bottom end point.
Image with alt text: A five-sided polygon is shown. The two sides forming the top of the form a shape like an Upper V. The side at the bottom is horizontal. The side at the left has a top endpoint higher and further left than the bottom end point. The side at the right has a top endpoint higher and further right than the bottom end point.
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The image that has reflectional, rotational, and point symmetry is:
A quadrilateral is shown. The top and bottom sides are horizontal and of unequal lengths. The other two sides appear to have the same length.
Therefore, the correct response is:
A quadrilateral is shown. The top and bottom sides are horizontal and of unequal lengths. The other two sides appear to have the same length.
Question
An 8-sided figure is shown. Its sides are all vertical and horizontal but they are all random lengths.
Which type of symmetry does the figure shown have?
(1 point)
Responses
line symmetry only
line symmetry only
point symmetry only
point symmetry only
point and line symmetry
point and line symmetry
no symmetry
no symmetry
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The 8-sided figure shown has line symmetry only.
Therefore, the correct response is line symmetry only.
Question
A left-parenthesis negative 3 comma negative 3 right-parenthesis right-arrow A prime is a glide reflection where the translation is left-parenthesis x comma y right-parenthesis right-arrow left-parenthesis x plus 5 comma y right-parenthesis, and the line of reflection is y = 1. What are the coordinates of A prime?
(1 point)
Responses
left-parenthesis 2 comma negative 3 right-parenthesis
Image with alt text: left-parenthesis 2 comma negative 3 right-parenthesis
left-parenthesis negative 3 comma 5 right-parenthesis
Image with alt text: left-parenthesis negative 3 comma 5 right-parenthesis
left-parenthesis 5 comma 1 right-parenthesis
Image with alt text: left-parenthesis 5 comma 1 right-parenthesis
left-parenthesis 2 comma 5 right-parenthesis
To find the coordinates of A prime after the glide reflection, we need to first apply the translation and then reflect the result across the line y = 1.
Starting with point A (-3, -3):
1. Apply the translation by adding 5 to the x-coordinate: (-3 + 5, -3) = (2, -3).
2. Reflect the translated point across the line y = 1 by negating the y-coordinate: (2, -3) reflects to (2, 5).
Therefore, the coordinates of A prime after the glide reflection are (2, 5).
The correct response is: (2, 5).
Describe the image of D first reflected across line l, then across line m.
The image shows two vertical lines with space between. Line l is to the left of line m. On the left side of line l is an upper case D. The D is oriented in the forwards direction with the vertical segment on the left of the arc.
To describe the image of D after being reflected across line l, then across line m, follow these steps:
1. Start with the original point of D before any reflections.
2. Reflect D across line l. This means that each point on D will have a corresponding point on the opposite side of line l, with the same distance from line l. The orientation and shape of D will remain the same.
3. Take the reflected image of D from step 2 and reflect it across line m. This means that each point on the reflected D will have a corresponding point on the opposite side of line m, with the same distance from line m. The orientation and shape of the reflected D will remain the same.
Since the image is described as a single uppercase D, with the same orientation and shape as the original D, the reflection across both lines l and m has no effect on the image. Therefore, the image of D after being reflected across line l, then across line m, is still D.
In other words, the image remains the same and is still the letter D.
Your teacher will grade your responses to ensure you receive proper credit for your answers.
Is one flag a translation image of the other, or a rotation image? Explain.
The image shows two identical flags on a coordinate plane.
Since the image shows two identical flags, we can determine whether one flag is a translation image or a rotation image of the other by comparing their positions and orientations.
If the flags have the same position and orientation, then they are translation images of each other. This means that one flag has been moved in a specific direction (up, down, left, or right) to obtain the other flag.
If the flags have different positions but the same orientation, then they are rotation images of each other. This means that one flag has been rotated around a specific point to obtain the other flag.
Without specific information or visual cues in the image, it is not possible to determine whether one flag is a translation image or a rotation image of the other.