Analytic Geometry in the Plane

Study equations of lines in the coordinate plane, including slopes, intersections, distances, and angle bisectors.

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BASIC DEFINITIONS
Basic Definitions
The core formulas for straight lines in the coordinate plane — the tools used throughout the problems below.
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1Problem 1 · General Equation of a Line Through Two PointsWrite the general equation of the line BCBC, given B(−2,−1)B(-2,-1) and C(4,3)C(4,3).Start →2Problem 2 · Perpendicular from a Point to a Line Through Two PointsIn the coordinate plane, let A(1,3)A(1,3), B(−2,−1)B(-2,-1), and C(4,3)C(4,3). Find the equation in general form of the line ADAD through AA perpendicular to BCBC.3Problem 3 · Bisectors of the Angles Between Two Perpendicular LinesIn the coordinate plane, let A(1,3)A(1,3), B(−2,−1)B(-2,-1), and C(4,3)C(4,3). Let ADAD be the line through AA perpendicular to BCBC. Find the equations of the two angle bisectors of lines BCBC and ADAD.4Problem 4 · Lines Through a Point Equidistant from Two PointsIn the coordinate plane, let A(1,3)A(1,3), B(−2,−1)B(-2,-1), and C(4,3)C(4,3). Find the equations of the two lines aa and bb through AA that are equidistant from BB and CC.5Problem 5 · tan φ Between Two Lines Equidistant from Two PointsCompute the tangent of the angle φ\varphi between the lines aa and bb through A(1,3)A(1,3) that are equidistant from B(−2,−1)B(-2,-1) and C(4,3)C(4,3).