Straight Lines

Formulas are organized based on their importance in the CAT exam.
1 Angle Between Two Lines
2 Midpoint Formula
3 Intercept on the $$y$$-Axis
4 Point of Division Using Parameter
5 Condition for Coincident Lines
6 Reflection of Point Over Line
7 Distance Between Parallel Lines
8 Section Formula
9 Distance from Point to Line
10 Line Through Intersection Parallel to a Given Line
11 Normal Form of a Straight Line
12 Distance Between Parallel Lines with Different Coefficients
13 Perpendicular Lines Condition
14 Angle Bisectors of a Pair of Lines Through the Origin
15 Parallel Lines Condition
16 Two-Point Form
17 Slope-Intercept Form
18 Angle Bisectors Through Distance Equality
19 Locus of a Point Equidistant from the Coordinate Axes
20 Distance Between Two Points
21 Area of a Triangle
22 Equation of a Line Passing Through a Fixed Point
23 Collinearity of Three Points
24 Coordinate Geometry of a Point
25 Perpendicular Distance Along a Normal
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 Equation of Line: Intercept Form
33 Equation of Line: Normal Form
34 Intercept Form from General Equation
35 Normal Form from General Equation
36 Slope of a Perpendicular Line
37 Reflection of a Point About a Line
38 Equation of Line: Slope-Intercept Form
39 Line Through a Point Perpendicular to a Given Line
40 Distance Between a Point and a Vertical Line
41 Distance Between a Point and a Horizontal Line
42 Locus of a Point Equidistant from Two Fixed Points
43 Equation of Line: Two-Point Form
44 Family of Lines Through the Intersection of Two Lines
45 Intercept on the $$x$$-Axis
46 Centroid Divides Each Median
47 Slope of a Line Joining Two Points
48 Inclination of a Line
49 Slope of Parallel Lines
50 Ratio of Areas of Triangles with Same Altitude
51 Distance Between Two Points on a Line
52 Ratio of Areas of Triangles with Same Base
53 Area of Triangle from Determinant
54 Obtuse Angle Between Two Lines
55 Angle Bisector Through Slopes
56 Equation of a Line with Given Slope Through Origin
57 Slope of Perpendicular Lines
58 Equation of a Line Through a Given Point with Given Inclination
59 Equation of a Line with Given Intercept on the $$x$$-Axis
60 Section Formula: Internal Division
61 Horizontal Line
62 Distance from Origin Using Normal Form
63 Equation of a Line at Distance $$p$$ from Origin
64 Centroid of a Triangle
65 Projection of a Point on the $$y$$-Axis
66 Reflection of a Point About the Origin
67 Locus of Points at Fixed Distance from a Given Line
68 Area of Triangle Using Base and Height
69 Area of Triangle Formed by Three Lines
70 Angle of Normal with the Line
71 Slope of a Line from General Equation
72 Coordinates of the Point Dividing a Segment in a Given Ratio
73 Slope of a Line Making Angle $$\theta$$
74 Equation of a Line Parallel to the $$x$$-Axis
75 Normal Vector of a Line
76 Symmetric Form of a Line
77 Point-Slope Form
78 Reflection of a Point About the $$y$$-Axis
79 Distance of a Point from the $$x$$-Axis
80 Equation of a Line Passing Through Two Fixed Points
81 Distance from Origin
82 Midpoint Formula
83 Angle Between Two Lines
84 Cross Product Condition for Parallel Directions
85 Slope from Direction Ratios
86 Condition for Perpendicular Lines in General Form
87 Distance Between Two Points Using Slope
88 Family of Lines Through a Common Point
89 Locus of a Point Equidistant from Two Intersecting Lines
90 Perpendicular Distance of a Line from Origin
91 Foot of Perpendicular from a Point to a Line
92 Coordinates of the Midpoint Through Section Formula
93 Equation of a Line Through Two Intercepts
94 Pythagorean Relation for Coordinate Differences
95 Condition for an Isosceles Triangle
96 $$x$$-Intercept from General Equation
97 Condition for Parallel Lines in General Form
98 Locus of Points at a Fixed Distance from the $$x$$-Axis
99 Equation of a Line Through Intersection and Parallel to Another Line
100 Normal Ratios of a Straight Line
101 Locus of a Point Equidistant from Two Fixed Points
102 Angle Between Two Lines in General Form
103 Equation of a Line Through Two Intersecting Lines' Point of Intersection
104 Direction Vector of a Line
105 Equation of a Line Parallel to the $$y$$-Axis Through a Point
106 Two-Point Parametric Form
107 Normal Form Parameters
108 Projection of a Point on the $$x$$-Axis
109 Parametric Form of a Line
110 Reflection of a Point About the $$x$$-Axis
111 Equation of a Line Parallel to a Vector
112 Locus of Points at a Fixed Distance from the $$y$$-Axis
113 Direction Cosines of a Line
114 Angle Between a Line and the $$x$$-Axis
115 Collinearity Through Slopes
116 Area of a Triangle Using Coordinate Differences
117 Orthocenter Condition
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 Distance Between Two Horizontal Lines
122 Equation of a Line Through Origin with Given Normal Ratios
123 Area of Triangle from Three Intercepts
124 Determinant Condition for Concurrency
125 Equation of a Line at a Given Distance from Another Line
126 Distance Between Two Points on a Horizontal Line
127 Equation of a Perpendicular Through a Point
128 Equation of a Line with Given Direction Vector
129 Equation of a Line Perpendicular to a Vector
130 Determinant Form for Intersection Coordinates
131 Intercept Form
132 Condition for a Parallelogram
133 Distance Between a Point and the Origin
134 Reflection in Normal Form
135 Condition for a Point to Lie on a Line
136 Angle Bisectors of Two Lines
137 Equation of a Line Using Direction Ratios
138 Equation of a Line Parallel to a Given Line Through a Point
139 Equation of Line: Point-Slope Form
140 Equation of a Line with Given Normal Vector
141 Distance Between Two Parallel Lines
142 General Equation of a Straight Line
143 Slope from General Equation
144 Area of Triangle Formed by Two Coordinate Axes
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