Answer: B. (x,y) → (2x - 4,2y-6)
Explanation:
A transformation that preserves both distance and angle measure is called an isometry. An isometry preserves distance because the distance between any two points in the pre-image is the same as the distance between their corresponding points in the image. An isometry also preserves angle measure because the angle between any two intersecting lines in the pre-image is the same as the angle between their corresponding lines in the image.
Option (B) represents a transformation that preserves both distance and angle measure. This transformation is a combination of a horizontal and a vertical stretch (or compression) with a scale factor of 2 and a translation of 4 units to the right and 6 units down. Since a stretch (or compression) preserves angle measure, and a translation preserves distance and angle measure, this transformation preserves both distance and angle measure, and therefore, is an isometry.
Option (A) represents a horizontal stretch with a scale factor of 2 and a translation of 4 units to the left and 6 units down. This transformation does not preserve distance, since the horizontal distances are multiplied by a factor of 2, and it does not preserve angle measure, since the angles between intersecting lines are not necessarily preserved.
Option (C) represents a 90-degree rotation followed by a reflection across the x-axis, which preserves angle measure, but does not preserve distance, since the distances between corresponding points are not necessarily the same.
Option (D) represents a 90-degree counterclockwise rotation followed by a reflection across the y-axis, which preserves angle measure, but does not preserve distance, since the distances between corresponding points are not necessarily the same.
Therefore, the correct answer is option (B).