Straight Lines

Formulas are organized based on their importance in the CAT exam.
1 Distance Between Parallel Lines
2 Parallel Lines Condition
3 Distance Between Two Parallel Lines
4 Angle Between Two Lines
5 Reflection of Point Over Line
6 Point of Division Using Parameter
7 Section Formula
8 Midpoint Formula
9 Condition for Coincident Lines
10 Normal Form of a Straight Line
11 Line Through Intersection Parallel to a Given Line
12 Perpendicular Lines Condition
13 Distance Between Two Horizontal Lines
14 Distance from Point to Line
15 Angle Bisectors of a Pair of Lines Through the Origin
16 Intercept on the $$y$$-Axis
17 Distance Between Parallel Lines with Different Coefficients
18 Two-Point Form
19 Slope-Intercept Form
20 Angle Bisectors Through Distance Equality
21 Locus of a Point Equidistant from the Coordinate Axes
22 Distance Between Two Points
23 Equation of a Line Passing Through a Fixed Point
24 Area of a Triangle
25 Collinearity of Three Points
26 Line Through Origin
27 Line Through Two Intercepts
28 Point-Slope Form Using General Coordinates
29 Determinant Form of a Straight Line
30 Area of the Intercept Triangle
31 Section Formula: External Division
32 Coordinate Geometry of a Point
33 Equation of Line: Intercept Form
34 Equation of Line: Normal Form
35 Intercept Form from General Equation
36 Normal Form from General Equation
37 Reflection of a Point About a Line
38 Equation of Line: Slope-Intercept Form
39 Slope of a Perpendicular Line
40 Line Through a Point Perpendicular to a Given Line
41 Distance Between a Point and a Vertical Line
42 Distance Between a Point and a Horizontal Line
43 Equation of Line: Two-Point Form
44 Family of Lines Through the Intersection of Two Lines
45 Perpendicular Distance Along a Normal
46 Centroid Divides Each Median
47 Slope of a Line Joining Two Points
48 Inclination of a Line
49 Slope of Parallel Lines
50 Locus of a Point Equidistant from Two Fixed Points
51 Area of Triangle from Determinant
52 Obtuse Angle Between Two Lines
53 Intercept on the $$x$$-Axis
54 Angle Bisector Through Slopes
55 Equation of a Line with Given Slope Through Origin
56 Ratio of Areas of Triangles with Same Base
57 Distance from Origin Using Normal Form
58 Equation of a Line at Distance $$p$$ from Origin
59 Centroid of a Triangle
60 Equation of a Line Through a Given Point with Given Inclination
61 Section Formula: Internal Division
62 Horizontal Line
63 Reflection of a Point About the Origin
64 Locus of Points at Fixed Distance from a Given Line
65 Slope of Perpendicular Lines
66 Area of Triangle Using Base and Height
67 Distance Between Two Points on a Line
68 Area of Triangle Formed by Three Lines
69 Slope of a Line from General Equation
70 Coordinates of the Point Dividing a Segment in a Given Ratio
71 Slope of a Line Making Angle $$\theta$$
72 Normal Vector of a Line
73 Symmetric Form of a Line
74 Angle of Normal with the Line
75 Point-Slope Form
76 Ratio of Areas of Triangles with Same Altitude
77 Projection of a Point on the $$y$$-Axis
78 Equation of a Line Parallel to the $$x$$-Axis
79 Cross Product Condition for Parallel Directions
80 Reflection of a Point About the $$y$$-Axis
81 Distance Between Two Points Using Slope
82 Equation of a Line Passing Through Two Fixed Points
83 Distance from Origin
84 Midpoint Formula
85 Coordinates of the Midpoint Through Section Formula
86 Angle Between Two Lines
87 Family of Lines Through a Common Point
88 Locus of a Point Equidistant from Two Intersecting Lines
89 Perpendicular Distance of a Line from Origin
90 Foot of Perpendicular from a Point to a Line
91 Pythagorean Relation for Coordinate Differences
92 Condition for an Isosceles Triangle
93 Equation of a Line Through Two Intercepts
94 $$x$$-Intercept from General Equation
95 Condition for Parallel Lines in General Form
96 Locus of Points at a Fixed Distance from the $$x$$-Axis
97 Normal Ratios of a Straight Line
98 Equation of a Line Through Intersection and Parallel to Another Line
99 Equation of a Line with Given Intercept on the $$x$$-Axis
100 Angle Between Two Lines in General Form
101 Slope from Direction Ratios
102 Condition for Perpendicular Lines in General Form
103 Equation of a Line Parallel to the $$y$$-Axis Through a Point
104 Two-Point Parametric Form
105 Parametric Form of a Line
106 Reflection of a Point About the $$x$$-Axis
107 Equation of a Line Parallel to a Vector
108 Locus of a Point Equidistant from Two Fixed Points
109 Direction Vector of a Line
110 Direction Cosines of a Line
111 Equation of a Line Through Two Intersecting Lines' Point of Intersection
112 Angle Between a Line and the $$x$$-Axis
113 Normal Form Parameters
114 Projection of a Point on the $$x$$-Axis
115 Locus of Points at a Fixed Distance from the $$y$$-Axis
116 Collinearity Through Slopes
117 Area of a Triangle Using Coordinate Differences
118 Equation of the $$x$$-Axis
119 Equation of the $$y$$-Axis
120 Equation of a Line Parallel to the $$x$$-Axis Through a Point
121 Equation of a Line Through Origin with Given Normal Ratios
122 Area of Triangle from Three Intercepts
123 Determinant Condition for Concurrency
124 Equation of a Line at a Given Distance from Another Line
125 Distance Between Two Points on a Horizontal Line
126 Equation of a Perpendicular Through a Point
127 Intercept Form
128 Condition for a Parallelogram
129 Equation of a Line with Given Direction Vector
130 Distance Between a Point and the Origin
131 Distance of a Point from the $$x$$-Axis
132 Orthocenter Condition
133 Equation of a Line Perpendicular to a Vector
134 Determinant Form for Intersection Coordinates
135 Reflection in Normal Form
136 Condition for a Point to Lie on a Line
137 Angle Bisectors of Two Lines
138 Equation of a Line with Given Normal Vector
139 Equation of a Line Using Direction Ratios
140 Slope from General Equation
141 General Equation of a Straight Line
142 Area of Triangle Formed by Two Coordinate Axes
143 Equation of Line: Point-Slope Form
144 Equation of a Line Parallel to a Given Line Through a Point
145 Distance Between Parallel Lines in Normal Form
146 Condition for an Equilateral Triangle
147 Direction Ratios from Slope
148 Point Equidistant from Two Lines
149 Ratio Corresponding to Parameter
150 Slope of a Line
151 Midpoint of the Intercepts
152 Equation of Perpendicular Bisector
153 Equation of a Line Through a Point with Given Normal
154 Length of a Segment from Its Projections
155 Distance of a Point from an Angle Bisector
156 Distance Between Two Vertical Lines
157 Locus of a Point Equidistant from a Fixed Point
158 Reflection and Midpoint Relation
159 Line Through a Point Perpendicular to a Given Direction
160 Projection of a Segment on the $$y$$-Axis
161 Projection of a Segment on the $$x$$-Axis
162 Collinearity Through Area
163 Length of the Intercept Segment
164 Distance Between Two Points Using Coordinates
165 Foot of Perpendicular in Normal Form
166 Distance Between Two Points in Parametric Form
167 Diagonals of a Parallelogram Bisect Each Other
168 Centroid Through Medians
169 Foot of Perpendicular Lies on the Given Line
170 Line Through a Point Parallel to a Given Line
171 Distance of a Point from the $$y$$-Axis
172 Vertical Line
173 Condition for Perpendicular Lines
174 Angle Between a Line and the $$y$$-Axis
175 Distance Between Two Non-Parallel Lines
176 Family of Parallel Lines
177 Line Through a Point Parallel to a Given Direction
178 Perpendicular Bisector Through Midpoint
179 Equation of a Median
180 Midpoint of a Horizontal Segment
181 Condition for a Quadrilateral to Be a Parallelogram
182 Area of a Triangle Using Two Side Vectors
183 Normal Ratios from Slope
184 Equation of a Line Through Intersection and Perpendicular to Another Line
185 Equation of a Line with Given Intercept on the $$y$$-Axis
186 Condition for Intersection of Two Lines
187 Family of Perpendicular Lines
188 Distance of a Point from a Line
189 Midpoint of a Vertical Segment
190 Median Length
191 Condition for Three Lines to Be Concurrent
192 Dot Product Condition for Perpendicular Lines
193 Acute Angle Between Two Lines
194 Slope of a Line
195 Centroid Divides a Median
196 Line Through Intersection Perpendicular to a Given Line
197 Equation of a Line Parallel to the $$y$$-Axis
198 Distance Between a Point and a Line Using Normal Form
199 Direction Ratios of a Straight Line
200 Distance Between Two Points on a Vertical Line
201 Equation of an Altitude
202 Slope in Terms of Inclination
203 Determinant Condition for Three Lines to Be Parallel
204 $$y$$-Intercept from General Equation
205 Fourth Vertex of a Parallelogram
206 Condition for Parallel Lines
207 Line Through Two Given Points
208 Condition for a Right-Angled Triangle
209 Incenter Condition
210 Distance of Origin from a Line in Intercept Form
211 Equation of a Line Through Origin with Given Direction Ratios
212 Slope of a Line in Normal Form
213 Intersection of Two Lines
214 Area of a Parallelogram
215 Altitude of a Triangle
216 Condition for a Line to Pass Through a Given Point
217 Circumcenter Condition
218 Median of a Triangle