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

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 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).

Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
problem_activity: Problem 1
Write an equation that models each point’s distance from the center of the circle, point
$$A$$
.
[IMG]
Problem 2
A circle has a center at the origin and contains the point (
$$2, \space \sqrt{5}$$
).
Write an equation of the circle.
Identify the radius of this circle.
Name two other points that lie on this circle.


correct_option_index: 2