Math / Geometry

Question2 Quadrilateral QRST is transformed by the rule $(x, y) \rightarrow(-x, y)$ a) How are the corresponding side lengths affected by the transformation?
The Corresponaling b) How are the corresponding angles affected by the transformation? $\qquad$ De c) How is the orientation of the quadrilateral affected? $\qquad$ reversed d) How is the area of the quadrilateral affected? e) How is the perimeter of the quadrilateral affected?

Studdy Solution

STEP 1

1. The transformation rule is $(x, y) \rightarrow (-x, y)$ .
2. The quadrilateral QRST is on a coordinate plane.
3. The transformation is a reflection across the y-axis.

STEP 2

1. Analyze the effect of the transformation on side lengths.
2. Analyze the effect of the transformation on angles.
3. Analyze the effect of the transformation on orientation.
4. Analyze the effect of the transformation on area.
5. Analyze the effect of the transformation on perimeter.

STEP 3

The transformation $(x, y) \rightarrow (-x, y)$ is a reflection across the y-axis. Reflections are isometries, which means they preserve distances. Therefore, the corresponding side lengths of the quadrilateral QRST are not affected by the transformation.

STEP 4

Since reflections are isometries, they also preserve angles. Thus, the corresponding angles of the quadrilateral QRST are not affected by the transformation.

STEP 5

The transformation $(x, y) \rightarrow (-x, y)$ reverses the orientation of the quadrilateral. If the original quadrilateral had a clockwise orientation, the transformed quadrilateral will have a counterclockwise orientation, and vice versa.

STEP 6

The area of a shape is invariant under reflections. Therefore, the area of the quadrilateral QRST is not affected by the transformation.

STEP 7

Since reflections preserve distances, the perimeter of the quadrilateral QRST is not affected by the transformation.

Was this helpful?

Studdy Solution

STEP 1

1. The transformation rule is $(x, y) \rightarrow (-x, y)$ .
2. The quadrilateral QRST is on a coordinate plane.
3. The transformation is a reflection across the y-axis.

STEP 2

1. Analyze the effect of the transformation on side lengths.
2. Analyze the effect of the transformation on angles.
3. Analyze the effect of the transformation on orientation.
4. Analyze the effect of the transformation on area.
5. Analyze the effect of the transformation on perimeter.

STEP 3

The transformation $(x, y) \rightarrow (-x, y)$ is a reflection across the y-axis. Reflections are isometries, which means they preserve distances. Therefore, the corresponding side lengths of the quadrilateral QRST are not affected by the transformation.

STEP 4

Since reflections are isometries, they also preserve angles. Thus, the corresponding angles of the quadrilateral QRST are not affected by the transformation.

STEP 5

The transformation $(x, y) \rightarrow (-x, y)$ reverses the orientation of the quadrilateral. If the original quadrilateral had a clockwise orientation, the transformed quadrilateral will have a counterclockwise orientation, and vice versa.

STEP 6

The area of a shape is invariant under reflections. Therefore, the area of the quadrilateral QRST is not affected by the transformation.

STEP 7

Since reflections preserve distances, the perimeter of the quadrilateral QRST is not affected by the transformation.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Studdy Solution

STEP 1

1. The transformation rule is (x,y)→(−x,y) (x, y) \rightarrow (-x, y) (x,y)→(−x,y).2. The quadrilateral QRST is on a coordinate plane.3. The transformation is a reflection across the y-axis.

STEP 2

1. Analyze the effect of the transformation on side lengths.2. Analyze the effect of the transformation on angles.3. Analyze the effect of the transformation on orientation.4. Analyze the effect of the transformation on area.5. Analyze the effect of the transformation on perimeter.

STEP 3

The transformation (x,y)→(−x,y) (x, y) \rightarrow (-x, y) (x,y)→(−x,y) is a reflection across the y-axis. Reflections are isometries, which means they preserve distances. Therefore, the corresponding side lengths of the quadrilateral QRST are not affected by the transformation.

STEP 4

Since reflections are isometries, they also preserve angles. Thus, the corresponding angles of the quadrilateral QRST are not affected by the transformation.

STEP 5

The transformation (x,y)→(−x,y) (x, y) \rightarrow (-x, y) (x,y)→(−x,y) reverses the orientation of the quadrilateral. If the original quadrilateral had a clockwise orientation, the transformed quadrilateral will have a counterclockwise orientation, and vice versa.

STEP 6

The area of a shape is invariant under reflections. Therefore, the area of the quadrilateral QRST is not affected by the transformation.

STEP 7

Since reflections preserve distances, the perimeter of the quadrilateral QRST is not affected by the transformation.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. The transformation rule is $(x, y) \rightarrow (-x, y)$ .
2. The quadrilateral QRST is on a coordinate plane.
3. The transformation is a reflection across the y-axis.

1. Analyze the effect of the transformation on side lengths.
2. Analyze the effect of the transformation on angles.
3. Analyze the effect of the transformation on orientation.
4. Analyze the effect of the transformation on area.
5. Analyze the effect of the transformation on perimeter.

The transformation $(x, y) \rightarrow (-x, y)$ is a reflection across the y-axis. Reflections are isometries, which means they preserve distances. Therefore, the corresponding side lengths of the quadrilateral QRST are not affected by the transformation.

The transformation $(x, y) \rightarrow (-x, y)$ reverses the orientation of the quadrilateral. If the original quadrilateral had a clockwise orientation, the transformed quadrilateral will have a counterclockwise orientation, and vice versa.