Question

Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Match each type of vector reflection with the matrix used to achieve it.

Answer 1

1. Reflection across the x-axis: [1 0 / 0 -1]

2. Reflection across the y-axis: [-1 0 / 0 1]

3. Reflection across the line y = x: [0 1 / 1 0]

Step-by-step explanation:

Vector reflection operations are achieved through matrix transformations. For a reflection across the x-axis, the matrix is [1 0 / 0 -1], where the first element represents the x-axis reflection, and the second element represents the y-axis reflection. Similarly, for reflection across the y-axis, the matrix is [-1 0 / 0 1]. These matrices are derived from the properties of reflection, where signs are changed to achieve the mirror effect.

When reflecting across the line y = x, the coordinates are swapped. This transformation is represented by the matrix [0 1 / 1 0]. The first column corresponds to the x-axis reflection, and the second column corresponds to the y-axis reflection. This matrix essentially swaps the x and y coordinates, achieving the desired reflection.

In summary, each type of vector reflection has a corresponding matrix that captures the transformation properties. The provided matrices can be used to achieve the specified reflections, ensuring accurate mapping between the mathematical representation and geometric transformation.