Question

What set of transformations are applied to parallelogram abcd to create a″b″c″d″?

Answer 1

The set of transformations applied to parallelogram ABCD to create A"B"C"D" is a translation and a reflection.

Step-by-step explanation:

The set of transformations applied to parallelogram ABCD to create A"B"C"D" is a translation and a reflection.

To create A"B"C"D", we start by translating parallelogram ABCD to a new position in the plane. This can be done by shifting all the points of ABCD by the same displacement vector. Then, we reflect the translated parallelogram across a line to create the final parallelogram A"B"C"D".

These transformations maintain the shape and size of the original parallelogram, but change its position and orientation in the plane.

Answer 2

In the context of vector transformations, parallelogram A'B'C'D' could be created from parallelogram ABCD by applying vector addition or subtraction using the parallelogram rule which involves translating vectors to have a common start point and constructing a new parallelogram to find resultant vectors.

Step-by-step explanation:

The question refers to the concept of vector transformations and the parallelogram rule in mathematics. This rule is a geometric method for vector addition and subtraction, where vectors are represented as sides of the parallelogram. The resulting vector is the diagonal of the parallelogram. To apply the parallelogram rule involves translating vectors so that they start at the same point, and then constructing a parallelogram where the opposite sides are equal and parallel, representing the vectors. The diagonal of the parallelogram then represents the resultant vector, and its length and direction can be measured using a ruler and protractor. This process allows for determining vector sums and differences graphically, without relying solely on algebraic methods or the law of cosines.

When a student asks about the set of transformations applied to create a parallelogram, they are likely referring to the process of translating and rotating the initial vectors (or sides of a parallelogram shape) to form the new parallelogram as needed by the problem's context.