Students calculate Euclidean distances between points and determine midpoints or missing endpoints of line segments using coordinate formulas, including integer, decimal, fractional, and radical values. They use slopes to identify parallel and perpendicular lines and write equations of lines through specified points, including horizontal and vertical cases. They apply coordinates, distance, midpoint, slope, and line equations to solve linear geometric problems involving collinearity, intersections, equal lengths, coordinate proofs, and classifications of triangles and quadrilaterals.