Question

Click to show whether each transformation on the coordinate plane preserves only angle or both distance and angle.

Option a: Preserves only angle
Option b: Preserves both distance and angle
Option c: Preserves only distance
Option d: None of the above

Answer 1

In mathematics, rotations, translations, and reflections on the coordinate plane are transformations that preserve both distance and angle. Dilations preserve only angles unless the scale factor is 1. The correct choice for a transformation that preserves both distance and angle is Option b.

Step-by-step explanation:

In mathematics, when we refer to transformations on the coordinate plane, we typically discuss translations, rotations, reflections, and dilation. The issue at hand is to determine which type of transformation preserves angle, distance, or both. Rotations and translations preserve both distances and angles, meaning the shape and size of figures are not altered during the transformation; therefore, they are considered isometries. However, when it comes to dilations (scale transformations), only the angles are preserved (assuming the scale factor is not 1), as the distances between points are changed proportionally. Reflections also preserve both distance and angle. Thus, for transformations on the coordinate plane that preserve both distance and angle, our choice would be Option b: Preserves both distance and angle.