options: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).

Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.

Find the point on a directed line segment between two given points that partitions the segment in a given ratio.

Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, Ö3) lies on the circle centered at the origin and containing the point (0, 2).
problem_activity: Task
On graph paper, sketch a line segment with end points $A=(0,2)$ and $B=(0,6)$. Plot all points $C=(x,y)$ such that the triangle ABC has an area of 6 square units.
What two basic geometric theorems are needed to solve this problem?


correct_option_index: 0