Foundation of Coordinate Geometry

Topics

Goods and Services Tax (G.S.T.)
- Tax and Its Computation
- Mathematical Study of GST (Goods and Services Tax)
- GST Structure for Calculations
- Computational Mechanisms under GST
- Input Tax Credit (ITC) in Mathematics
- E-way Bill in GST Sums
- Examples based on GST Calculations
Commercial Mathematics
Compound Interest
- Compound Interest as a Repeated Simple Interest Computation with a Growing Principal
- Use of Compound Interest in Computing Amount Over a Period of 2 Or 3-years
- Use of Formula
- Finding CI from the Relation CI = A – P
Banking
- Money and Banking in Arithmetic
- Mathematics of Recurring Deposit (R.D.)
Algebra
Shares and Dividends
- Shares
- Formulae for Shares and Dividends
- Examples based on Shares and Dividends
Geometry
Mensuration
Linear Inequations
- Linear Inequations
- Method of Solving a Linear Inequality
- Representation of Inequalities
- Combining Inequalities
- Product of Two Linear Expressions
Trigonometry
Quadratic Equations
- Quadratic Equations
- Method of Solving a Quadratic Equation
- Factorisation Method
- Quadratic Formula (Shreedharacharya's Rule)
- Nature of Roots of a Quadratic Equation
- Equations Reducible to Quadratic Equations
Statistics
Ratio and Proportion
- Ratio
- Ratio in Lowest Terms
- All About Ratios: Dividing, Comparing, and Modifying Quantities
- Commensurable and Incommensurable Quantities
- Composition of Ratios
- Proportion
- Concept of Continued Proportion
- Properties of Proportion
- Direct Applications of Ratio and Proportion
Factorisation of Polynomials
- Function and Polynomial
- Division Algorithm for Polynomials
- Remainder Theorem
- Factor Theorem
- Applications of Factor Theorem
Probability
Matrices
- Concept of Matrices
- Types of Matrices
- Equality of Matrices
- Compatibility of Matrices
- Transpose of a Matrix
- Operations on Matrices> Addition and Subtraction of Matrices
- Operations on Matrices> Matrix Multiplication
- Operations on Matrices>Scalar Multiplication
Arithmetic and Geometric Progression
- Sequence, Series, and Progression
- Arithmetic Progression (A.P.)
- General Term of an Arithmetic Progression
- Sum of First ‘n’ Terms of an Arithmetic Progressions
- Three or More Terms in Arithmetic Progression (A.P.)
- Arithmetic Mean in A.P.
- Properties of an Arithmetic Progression
Co-ordinate Geometry
- Foundation of Coordinate Geometry
- Advanced Concept of Reflection in Mathematics
- Invariant Points
- Combination of Reflections
- Using Graph Paper for Reflection
Symmetry
Similarity
- Similarity and Congruency of Figures
- Similarity as a Size Transformation
- Applications to Maps and Models
- Similarity of Triangles (Corresponding Sides & Angles)
- Criteria for Similarity of Triangles
- Basic Proportionality Theorem
- Relation Between the Areas of Two Triangles
Loci
- Locus
- Points Equidistant from Two Given Points
- Points Equidistant from Two Intersecting Lines
- Summary of Important Results on Locus
- Important Points on Concurrency in a Triangle
Circles
- Geometrical Concepts Related to a Circle
- Chord
- Arc of the Circle
- Segment of a Circle
- Theorems on Angles in a Circle
- Cyclic Quadrilateral and Concyclic Points
- Some Important Results on Circles
- Advanced Theorems Related to Circles
Tangent and Secant Properties
- Secant and Tangent
- Tangent and Secant Properties
- Intersecting Chords and Tangents
- Alternate Segment Property
Constructions
- Construction of Tangents to a Circle
- Construction of Two Tangents to a Circle
- Circumcircle of a Triangle
- Incircle of a Triangle
- Circumscribed Circle of a Regular Polygon
- Inscribed Circle of a Regular Polygon
Area and Volume of Solids (Cylinder, Cone and Sphere)
- Mensuration of Cylinder
- Hollow Cylinder
- Mensuration of Cones
- Mensuration of a Sphere
- Hemisphere
- Conversion of Solids
- Solid Figures
- Problems on Mensuration
Trigonometrical Identities
- Trigonometric Ratios
- Relation Among Trigonometric Ratios
- Trigonometric Identities (Square Relations)
- Elimination of Trigonometrical Ratios
- Trigonometric Ratios of Complementary Angles
- Application of Trigonometric Tables
Heights and Distances
- Angles of Elevation and Depression
- Problems based on Elevation and Depression
Statistics : basic concepts, Mean, Median, Mode. Histograms and Ogive
- Frequency Distribution and Its Applications
- Concepts of Statistics
- Histograms
- Frequency Polygon
- Cumulative Frequency and Cumulative Frequency Table
- Ogives (Cumulative Frequency Curve)
Probability
- Concept of Probability
- Elementary Types of Events and Properties of Probability
- Measurement of Probability
- Standard Results for Outcomes in Probability
- Problems based on Probability

Estimated time: 2 minutes

CBSE: Class 10
CISCE: Class 10

Definition: Co-ordinate Axes

The two mutually perpendicular number lines intersecting each other at their zeroes are called rectangular axes or coordinate axes, or axes of reference.

Maharashtra State Board: Class 12

Formula: Foundation of Coordinate Geometry

Sr. No.	Name	Condition	Formula
i.	Distance Formula	Two points P(x₁, y₁), Q(x₂, y₂)	\[\mathrm{d(PQ)}=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}\]
a.	Internal Division	P divides AB in the ratio m: n	\[\mathrm{P\equiv\left(\frac{mx_{2}+nx_{1}}{m+n},\frac{my_{2}+ny_{1}}{m+n}\right)}\]
b.	Midpoint Formula	P is the midpoint of AB	\[\mathrm{P}\equiv\left(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2}\right)\]
c.	External Division	P divides AB externally in m: n	\[\mathrm{P\equiv\left(\frac{mx_{2}-nx_{1}}{m-n},\frac{my_{2}-ny_{1}}{m-n}\right)}\]
iii.	Centroid Formula	Triangle with vertices A, B, C	\[\left(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3}\right)\]

CBSE: Class 10
CISCE: Class 10

Definition: Co-ordinates

The position of a point in a plane is expressed by a pair of numbers, one concerning the x-axis and the other concerning the y-axis. called co-ordinates.

x → distance from y-axis (abscissa)
→ distance from x-axis (ordinate)

CISCE: Class 10

Key Points: Co-ordinate Geometry

Sign Convention

Right of y-axis →
Left of y-axis →
Above x-axis →
Below x-axis →

Standard Line Results

→ y-axis
→ x-axis
→ line parallel to the y-axis
→ line parallel to the x-axis

Quadrant Reminder

Quadrant	Sign of (x, y)
I	(+, +)
II	(−, +)
III	(−, −)
IV	(+, −)

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Foundation of Coordinate Geometry

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Topics

Goods and Services Tax (G.S.T.)

Commercial Mathematics

Compound Interest

Banking

Algebra

Shares and Dividends

Geometry

Mensuration

Linear Inequations

Trigonometry

Quadratic Equations

Statistics

Ratio and Proportion

Factorisation of Polynomials

Probability

Matrices

Arithmetic and Geometric Progression

Co-ordinate Geometry

Symmetry

Similarity

Loci

Circles

Tangent and Secant Properties

Constructions

Area and Volume of Solids (Cylinder, Cone and Sphere)

Trigonometrical Identities

Heights and Distances

Statistics : basic concepts, Mean, Median, Mode. Histograms and Ogive

Probability

Definition: Co-ordinate Axes

Formula: Foundation of Coordinate Geometry

Definition: Co-ordinates

Key Points: Co-ordinate Geometry

Video Tutorials

Shaalaa.com | Coordinate Geometry Exercise 7.1 Q1

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