options: 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.

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.
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: 0