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When describing a rotation, which of the following directions is applicable for a rotation?(1 point)

Responses

counterclockwise
counterclockwise

up
up

right
right

down

Use the image to answer the question.

Two triangles are drawn on a coordinate plane. Triangle A B C is drawn with a solid line and is in quadrant 3. Triangle A prime B prime C prime is drawn with a dotted line and is in quadrant 4.

Describe the transformation in the diagram.

(1 point)
Responses

90°
clockwise rotation about the origin
90 degrees clockwise rotation about the origin

270°
counterclockwise rotation about the origin
270 degrees counterclockwise rotation about the origin

180°
counterclockwise rotation about the origin
180 degrees counterclockwise rotation about the origin

90°
counterclockwise rotation about the origin
90 degrees counterclockwise rotation about the origin
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Question
A segment has endpoints X(−10,0)
and Y(−2,6)
. Consider its image after a 180°
(counterclockwise) rotation about the origin. Select the coordinates of Y′
.(1 point)
Responses

Y′(6,−2)
upper Y prime left parenthesis 6 comma negative 2 right parenthesis

Y′(−6,2)
upper Y prime left parenthesis negative 6 comma 2 right parenthesis

Y′(−2,−6)
upper Y prime left parenthesis negative 2 comma negative 6 right parenthesis

Y′(2,−6)
upper Y prime left parenthesis 2 comma negative 6 right parenthesis
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Question
Use the image to answer the question.

A quadrilateral is plotted on a coordinate plane with both the axes ranging from negative 10 to 10.

Imagine a 90°
(counterclockwise) rotation about the origin of the figure in the image. Select the coordinate of D′
.

(1 point)
Responses

(4,−8)
left parenthesis 4 comma negative 8 right parenthesis

(8,4)
left parenthesis 8 comma 4 right parenthesis

(8,−4)
left parenthesis 8 comma negative 4 right parenthesis

(−8,4)
left parenthesis negative 8 comma 4 right parenthesis
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Question
Use the image to answer the question.

A quadrilateral is plotted a coordinate plane with both the axes ranging from negative 6 to 6.

Imagine a counterclockwise rotation of 270°
about the origin of the figure. Choose the coordinate of A′
.

(1 point)
Responses

(−1,−2)
left parenthesis negative 1 comma negative 2 right parenthesis

(1,1)
left parenthesis 1 comma 1 right parenthesis

(1,2)
left parenthesis 1 comma 2 right parenthesis

(2,−1)
left parenthesis 2 comma negative 1 right parenthesis
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1 answer

Let's go through each of your questions one by one:

  1. Direction Applicable for a Rotation: The most commonly applicable direction for a rotation in mathematics (specifically in a coordinate plane) is counterclockwise.

  2. Transformation of the Triangles: Since Triangle A'B'C' is in quadrant 4 and Triangle ABC is in quadrant 3, it has undergone a 90° clockwise rotation about the origin. Thus, the correct response is: 90° clockwise rotation about the origin.

  3. Rotation of Segment XY: To find the coordinates of Y' after a 180° rotation about the origin, we change the signs of both coordinates. The coordinates of Y are (-2, 6). After the rotation, Y' becomes (2, -6). Therefore, the correct response is: Y′(2,−6).

  4. Coordinate of D' after 90° Counterclockwise Rotation: To perform a 90° counterclockwise rotation, you switch the coordinates and change the sign of the new x-coordinate. Assuming the coordinates of D before rotation are (x, y), they will become (-y, x). Without the specific coordinates of D given, I can't provide the exact answer, but based on the options: If D is at (4, -8), it will rotate to (8, 4) (which matches one of the options). Therefore, if D was at (4, -8), the correct response is: (8, 4).

  5. Coordinate of A′ after 270° Counterclockwise Rotation: A 270° counterclockwise rotation is equivalent to a 90° clockwise rotation. Using the same method as before, if A has coordinates (x, y), after a 270° rotation, the new coordinates will be (y, -x). Assuming we apply this to the listed options for A:

    • If A was, for instance, (1, 2), it rotates to (2, -1). (2,−1) seems to be the most consistent answer based on the rotation method.

If there are any additional details or questions you have for clarification, feel free to ask!