Rotations Quick Check

Question

Rotations Quick Check
1 of 51 of 5 Items
Question
Demonstrating the properties of rotations, if a line segment with endpoints  (0,−3)
(
0
,
−
3
)
  and  (0,−7)
(
0
,
−
7
)
  is rotated  90°
90
°
  clockwise, what is an endpoint of this rotated segment?(1 point)
Responses

(3, 0)
(
3
,
 
0
)
  left parenthesis 3 comma 0 right parenthesis

(0, 7)
(
0
,
 
7
)
  left parenthesis 0 comma 7 right parenthesis

(−3, 0)
(
−
3
,
 
0
)
left parenthesis negative 3 comma 0 right parenthesis

(0, 3)
(
0
,
 
3
)
  left parenthesis 0 comma 3 right parenthesis

Rotations Quick Check
2 of 52 of 5 Items
Question
Rotate a point on a line at  (−4, 6)
(
−
4
,
 
6
)
   180°
180
°
  counterclockwise. What is the resulting point?(1 point)
Responses

(−6, 4)
(
−
6
,
 
4
)
  left parenthesis negative 6 comma 4 right parenthesis

(−4, −6)
(
−
4
,
 
−
6
)
  left parenthesis negative 4 comma negative 6 right parenthesis

(6, −4)
(
6
,
 
−
4
)
  left parenthesis 6 comma negative 4 right parenthesis

(4, −6)
(
4
,
 
−
6
)
left parenthesis 4 comma negative 6 right parenthesis
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Rotations Quick Check
3 of 53 of 5 Items
Question
Jack discovers that the orientation of a triangle is counterclockwise. He then reflects the triangle over the  y
y
 -axis. What is the orientation of the reflected figure?(1 point)
Responses

There is not enough information to tell.
There is not enough information to tell.

The reflected figure has a counterclockwise orientation.
The reflected figure has a counterclockwise orientation.

The reflected figure has a clockwise orientation.
The reflected figure has a clockwise orientation.

The orientation could be clockwise or counterclockwise depending on how you do the reflection.
The orientation could be clockwise or counterclockwise depending on how you do the reflection.
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Rotations Quick Check
4 of 54 of 5 Items
Question
If a triangle with vertices  (4, 3)
(
4
,
 
3
)
 ,  (8, 3)
(
8
,
 
3
)
 , and  (7, 5)
(
7
,
 
5
)
  is translated to the right 4 units and down 2 units, what are the vertices of the translated figure?(1 point)
Responses

(8, 5)
(
8
,
 
5
)
, (12, 5)
(
12
,
 
5
)
, and (11, 7)
(
11
,
 
7
)
  left parenthesis 8 comma 5 right parenthesis ,  left parenthesis 12 comma 5 right parenthesis , and  left parenthesis 11 comma 7 right parenthesis

(0, 1)
(
0
,
 
1
)
, (4, 1)
(
4
,
 
1
)
, and (3, 3)
(
3
,
 
3
)
  left parenthesis 0 comma 1 right parenthesis ,  left parenthesis 4 comma 1 right parenthesis , and  left parenthesis 3 comma 3 right parenthesis

(8, 3)
(
8
,
 
3
)
, (12, 3)
(
12
,
 
3
)
, and (11, 5)
(
11
,
 
5
)
  left parenthesis 8 comma 3 right parenthesis ,  left parenthesis 12 comma 3 right parenthesis , and  left parenthesis 11 comma 5 right parenthesis

(8, 1)
(
8
,
 
1
)
, (12, 1)
(
12
,
 
1
)
, and (11, 3)
(
11
,
 
3
)
left parenthesis 8 comma 1 right parenthesis ,  left parenthesis 12 comma 1 right parenthesis , and  left parenthesis 11 comma 3 right parenthesis
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Which transformation(s) will result in a figure that has the same orientation as the original figure?(1 point)
Responses

translation, rotation, and reflection
translation, rotation, and reflection

translation only
translation only

translation and rotation
translation and rotation

reflection only

GPT-4o mini · Answer

Let's go through each question step by step.

Question 1

To rotate the line segment with endpoints (0, -3) and (0, -7) 90° clockwise:

The original points are both on the y-axis.
For a 90° clockwise rotation, the transformation of a point (x, y) becomes (y, -x).
For point (0, -3): \[(y, -x) = (-3, 0)\]
For point (0, -7): \[(y, -x) = (-7, 0)\]

One endpoint of the rotated segment is (0, 3). Therefore, the answer is:

(−3, 0) (the other endpoint).

Question 2

To rotate the point (-4, 6) 180° counterclockwise:

The transformation for 180° rotation is (x, y) → (-x, -y).
Thus, \[(-4, 6) \rightarrow (4, -6)\]

The resulting point is:

(4, -6)

Question 3

If Jack reflects a counterclockwise oriented triangle over the y-axis:

Reflections over the y-axis flip the orientation.
Thus, if the original orientation is counterclockwise, the reflection will be clockwise.

The answer is:

The reflected figure has a clockwise orientation.

Question 4

For the triangle's vertices:

Original points: (4, 3), (8, 3), and (7, 5).
Translation: right 4 units and down 2 units.

Calculating the new vertices:

(4, 3) → (4 + 4, 3 - 2) = (8, 1)
(8, 3) → (8 + 4, 3 - 2) = (12, 1)
(7, 5) → (7 + 4, 5 - 2) = (11, 3)

The translated vertices are:

(8, 1), (12, 1), and (11, 3).

Question 5

Transformations that result in a figure with the same orientation as the original:

Translation and rotation maintain the orientation.
Reflection changes the orientation.

Therefore, the answer is:

translation and rotation.

Summary of Answers

(−3, 0)
(4, −6)
The reflected figure has a clockwise orientation.
(8, 1), (12, 1), and (11, 3)
translation and rotation