Q1: What is the set of points at equal Manhattan distance to some point?
It is exactly a circle to point p, which the center is on the point p.
Q2: How can the distance between two line segments be realized?
Find the minimum distance between two points that are part of each line.
see #1.
Q3: How many intersection points can a line and a circle have?
0, 1 or 2.
Q4: What are the possible outcomes of the intersection of a rectangle and a quadrant?
nothing, rectangle or polygon.
Q5: What is the maximum number of intersection points of a line and a simple polygon with 10 vertices (trick question)?
don't know.
Q6: What is the maximum number of intersection points of a line and a simple polygon boundary with 10 vertices (still a trick question)?
don't know.
Q7: What is the maximum number of edges of a simple polygon boundary with 10 vertices that a line can intersect?
don't know.
Q8: Suppose that a simple polygon with n vertices is given; the vertices are given in counterclockwise order along the boundary. Give an efficient algorithm to determine all edges that are intersected by a given line.
Q9: Which of the following shapes are convex? Point, line segment, line, circle, disk, quadrant?
All, in addition to Point.
For any subset of the plane (set of points, rectangle, simple polygon), its convex hull is the smallest convex set that contains that subset.
Give an algorithm that computes the convex hull of any given set of n points in the plane efficiently
see pseudo code
Reference: Introduction and convex hulls