A triangle with vertices at (1,1), (4,1), and (1,3) is transformed to a triangle with vertices at (3,1), (6,1), and (3,3). Which transformation was applied?

Question

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1 point
Translation 2 units to the right
Reflection over the y-axis
Rotation 90 degrees clockwise about the origin
Translation 2 units up

Answer 1

To determine the transformation applied to the triangle with vertices at (1,1), (4,1), and (1,3) to get the triangle with vertices at (3,1), (6,1), and (3,3), we can look at the changes in the coordinates of the vertices.

• The first vertex (1,1) is transformed to (3,1). This indicates a horizontal movement of +2 units to the right.
• The second vertex (4,1) is transformed to (6,1). This also indicates a horizontal movement of +2 units to the right.
• The third vertex (1,3) is transformed to (3,3). Again, this indicates a horizontal movement of +2 units to the right.

Since all vertices have been moved 2 units to the right with no change in their vertical position, the transformation applied is a translation 2 units to the right.

So the correct option is: Translation 2 units to the right.

Answer 2

A triangle with vertices at (2,3), (3,5), and (5,3) is transformed to a triangle with vertices at (4,6), (5,8), and (7,6). Which transformation was applied?
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1 point
Translation 2 units up and 2 units right
Translation 2 units up and 2 units left
Rotation 180 degrees about the origin
Rotation 90 degrees clockwise about the origin

Answer 3

To determine the transformation applied to the triangle with vertices at (2,3), (3,5), and (5,3) to get the triangle with vertices at (4,6), (5,8), and (7,6), we can analyze the changes in the coordinates of the vertices:

1. The first vertex (2,3) is transformed to (4,6).

   • Change in x-coordinate: \(4 - 2 = 2\) (moved 2 units to the right)
   • Change in y-coordinate: \(6 - 3 = 3\) (moved 3 units up)

2. The second vertex (3,5) is transformed to (5,8).

   • Change in x-coordinate: \(5 - 3 = 2\) (moved 2 units to the right)
   • Change in y-coordinate: \(8 - 5 = 3\) (moved 3 units up)

3. The third vertex (5,3) is transformed to (7,6).

   • Change in x-coordinate: \(7 - 5 = 2\) (moved 2 units to the right)
   • Change in y-coordinate: \(6 - 3 = 3\) (moved 3 units up)

From the analysis, all vertices have been moved 2 units to the right and 3 units up.

Therefore, the transformation that was applied is: Translation 2 units up and 2 units right.

(Note: The original question choices might have a mismatch in the description of the movements, as there is a movement up of 3 units indicated by the changes, but in the provided answer options, you have asked for 2 units up. Be sure to verify any additional context surrounding the question.)

Answer 4

A square with vertices at (3,3), (6,3), (6,6), and (3,6) is transformed to a square with vertices at (−3,−3), (−6,−3), (−6,−6), and (−3,−6). Which transformation was applied?
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1 point
Translation 6 units left and 6 units down
Translation 6 units right and 6 units up
Rotation 180 degrees about the origin
Rotation 90 degrees clockwise about the origin

Answer 5

To analyze the transformation from the square with vertices at (3,3), (6,3), (6,6), and (3,6) to the square with vertices at (−3,−3), (−6,−3), (−6,−6), and (−3,−6), let’s look into the changes in the coordinates of the vertices.

1. The first vertex (3,3) is transformed to (−3,−3).

   • Change: \( x \) changes from \(3\) to \(-3\) (which is a change of -6).
   • Change: \( y \) changes from \(3\) to \(-3\) (which is also a change of -6).

2. The second vertex (6,3) is transformed to (−6,−3).

   • Change: \( x \) changes from \(6\) to \(-6\) (which is a change of -12).
   • Change: \( y \) changes from \(3\) to \(-3\) (which is a change of -6).

3. The third vertex (6,6) is transformed to (−6,−6).

   • Change: \( x \) changes from \(6\) to \(-6\) (which is a change of -12).
   • Change: \( y \) changes from \(6\) to \(-6\) (which is a change of -12).

4. The fourth vertex (3,6) is transformed to (−3,−6).

   • Change: \( x \) changes from \(3\) to \(-3\) (which is a change of -6).
   • Change: \( y \) changes from \(6\) to \(-6\) (which is a change of -12).

All vertices are being moved from the first quadrant to the third quadrant, and in particular, each coordinate is being negated (meaning both \(x\) and \(y\) values are flipped to their negatives).

This transformation corresponds to a rotation of 180 degrees about the origin.

Hence, the correct answer is: Rotation 180 degrees about the origin.

Answer 6

A pentagon with vertices at (1,1), (2,3), (4,3), (5,1), and (3,0) is transformed to a pentagon with vertices at (1,−1), (2,−3), (4,−3), (5,−1), and (3,0). Which transformation was applied?
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1 point
Rotation 180 degrees about the origin
Rotation 90 degrees counterclockwise about the origin
Translation 2 units down
Reflection over the x-axis

Answer 7

To determine the transformation applied to the pentagon with vertices at (1,1), (2,3), (4,3), (5,1), and (3,0) to get the pentagon with vertices at (1,−1), (2,−3), (4,−3), (5,−1), and (3,0), we should analyze the changes in the coordinates of the vertices.

Let's look at each vertex:

1. The first vertex (1,1) is transformed to (1,−1).

   • Change in y-coordinate: \( -1 - 1 = -2 \) (moved 2 units down)

2. The second vertex (2,3) is transformed to (2,−3).

   • Change in y-coordinate: \( -3 - 3 = -6 \) (moved 6 units down)

3. The third vertex (4,3) is transformed to (4,−3).

   • Change in y-coordinate: \( -3 - 3 = -6 \) (moved 6 units down)

4. The fourth vertex (5,1) is transformed to (5,−1).

   • Change in y-coordinate: \( -1 - 1 = -2 \) (moved 2 units down)

5. The fifth vertex (3,0) remains the same, (3,0).

From the analysis, we can see that the vertices have undergone a transformation where:

• The y-coordinates of the points (except for the point (3,0), which remains the same) have been negated.

This suggests that the transformation applied is a reflection over the x-axis.

Therefore, the correct answer is: Reflection over the x-axis.

Answer 8

A rectangle with vertices at (2,3), (5,3), (5,6), and (2,6) is transformed to a rectangle with vertices at (2,−3), (5,−3), (5,−6), and (2,−6). Which transformation was applied?
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1 point
Reflection over the x-axis
Reflection over the y-axis
Rotation 180 degrees about the origin
Translation 6 units down

Answer 9

To determine the transformation applied to the rectangle with vertices at (2,3), (5,3), (5,6), and (2,6) to get the rectangle with vertices at (2,−3), (5,−3), (5,−6), and (2,−6), we will analyze the changes in the coordinates of the vertices.

1. The first vertex (2,3) is transformed to (2,−3).

   • The x-coordinate remains the same: \(2 \rightarrow 2\).
   • The y-coordinate changes from \(3\) to \(-3\) (which is a reflection over the x-axis).

2. The second vertex (5,3) is transformed to (5,−3).

   • The x-coordinate remains the same: \(5 \rightarrow 5\).
   • The y-coordinate changes from \(3\) to \(-3\) (which is a reflection over the x-axis).

3. The third vertex (5,6) is transformed to (5,−6).

   • The x-coordinate remains the same: \(5 \rightarrow 5\).
   • The y-coordinate changes from \(6\) to \(-6\) (which is a reflection over the x-axis).

4. The fourth vertex (2,6) is transformed to (2,−6).

   • The x-coordinate remains the same: \(2 \rightarrow 2\).
   • The y-coordinate changes from \(6\) to \(-6\) (which is a reflection over the x-axis).

Since all the y-coordinates have been negated while the x-coordinates remain unchanged, this indicates that the transformation involved reflecting the rectangle over the x-axis.

Therefore, the correct answer is: Reflection over the x-axis.