Math  /  Geometry

Question2 Quadrilateral QRST is transformed by the rule (x,y)(x,y)(x, y) \rightarrow(-x, y) to create quadrilateral QRSTQ^{\prime} R^{\prime} S^{\prime} T^{\prime}. a) How are the corresponding side lengths affected by the transformation?
The Corresponaling b) How are the corresponding angles affected by the transformation? \qquad continue \qquad 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 given is a reflection over the y-axis.
2. The original quadrilateral is denoted as QRST.
3. The transformed quadrilateral is denoted as QRST Q^{\prime} R^{\prime} S^{\prime} T^{\prime} .

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 area.
4. Analyze the effect of the transformation on perimeter.

STEP 3

The transformation rule (x,y)(x,y)(x, y) \rightarrow (-x, y) is a reflection over the y-axis. Reflections preserve distances between points. Therefore, the corresponding side lengths of the quadrilateral are unaffected by the transformation.

STEP 4

Reflections preserve angles between lines. Therefore, the corresponding angles of the quadrilateral are unaffected by the transformation.

STEP 5

The area of a shape is preserved under reflections because the shape's dimensions and orientation relative to the axes remain unchanged. Therefore, the area of the quadrilateral is unaffected by the transformation.

STEP 6

The perimeter of a shape is the sum of its side lengths. Since the side lengths are unaffected by the reflection, the perimeter of the quadrilateral is also unaffected by the transformation.
The transformation does not affect the side lengths, angles, area, or perimeter of the quadrilateral.

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