The correct answer is: C. both a and b.
Euclidean distance is the most common distance metric used in geometric models. It is defined as the square root of the sum of the squared differences between the coordinates of the two points. Manhattan distance, also known as taxicab distance, is another common distance metric used in geometric models. It is defined as the sum of the absolute differences between the coordinates of the two points.
Both Euclidean distance and Manhattan distance are powerful distance metrics that can be used to measure the distance between two points in a geometric model. They are both based on the idea of measuring the length of a line segment between the two points. However, they differ in how they measure the length of the line segment. Euclidean distance measures the length of the line segment as the shortest distance between the two points, while Manhattan distance measures the length of the line segment as the sum of the lengths of the horizontal and vertical segments between the two points.
The choice of which distance metric to use depends on the specific application. Euclidean distance is typically used when the distance between two points is interpreted as a measure of the physical distance between them. Manhattan distance is typically used when the distance between two points is interpreted as a measure of the cost of traveling between them.