Coordinate Geometry Class 10th Notes - Free NCERT Class 10 Maths Chapter 7 Notes

Coordinate Geometry Class 10th Notes - Free NCERT Class 10 Maths Chapter 7 Notes - Download PDF

Edited By Safeer PP | Updated on Mar 19, 2022 12:15 PM IST

Coordinate geometry is the NCERT chapter which deals with distance formula. The NCERT Class 10 Maths chapter 7 notes covers an outline of the chapter coordinate geometry. The main topics covered in coordinate geometry Class 10 notes are section formulae, abscissa and ordinates. Class 10 Maths chapter 7 notes includes FAQ or frequently asked questions about the chapter. These topics can also be downloaded from the Coordinate Geometry Class 10 notes pdf download option.

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This Story also Contains

Cartesian Coordinate System
Distance From Origin
Section Formula
Midpoint Formula
Area of a Triangle
Centroid of a Triangle
Significance of NCERT Class 10 Maths Chapter 7 Notes
Class 10 Chapter Wise Notes
NCERT Solutions of Cass 10 Subject Wise
NCERT Class 10 Exemplar Solutions for Other Subjects:

Also, students can refer,

Cartesian Coordinate System

In the Cartesian coordinate system, two number lines that are perpendicular to each other,, the x-axis (horizontal) and y-axis (vertical) represents the two variables. These two perpendicular lines are called the coordinate axis.

The intersection point of these two lines is known as the center or the origin of the coordinate plane. Its coordinates are (0,0).
Point on this coordinate plane is represented by an ordered pair of numbers. Let (a, b) be an ordered pair then a is the x-coordinate and b is the y-coordinate.
The distance of any point from the y-axis is called x-coordinate or abscissa and the distance of any point from the x-axis is called y-coordinate or ordinate.
The Cartesian plane has four quadrants I, II, III and IV.

Cartesian Coordinate System

Equation of a Straight Line

An equation of line is used to plot a graph of that line on a cartesian plane.

Slope intercept form

y = mx +b

Where, m is the slope of the line, b = y-intercept.

m=change in ychange in x

Equation of a Straight Line

Distance formula

The distance between two points A(x₁,y₁) and B(x₂,y₂) is calculated by the formula:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Distance formula

Distance From Origin

To find the distance of any point from the origin, one point is P(x,y) and the other point is the origin itself, which is O(0,0). According to the above distance formula, it will be:

$OP=\sqrt{x^2+y^2}$

Section Formula

Let F(x, y) is any point on the line segment AB, that divides AB in the ratio of m: n, then the coordinates of the point F(x, y) will be:

x=(mx₂+nx₁)_/(m+n) and

y=(my₂+ny₁)/m+n

then the coordinates of the point P(x, y) will be

Midpoint Formula

If F(x, y) is the mid-point of the line segment AB, that divides AB in the ratio of 1:1, then the coordinates of the point F(x, y) will be:

x=(x₂+x₁)/2 and y=(y₂+y₁)/2

Area of a Triangle

Area of a triangle

Area of triangle ABC = Area of trapezium ABQP + Area of trapezium APRC – Area of trapezium BQRC.

Area of a trapezium=12(sum of parallel sides) (distance between them)

Therefore,

Area of ABC

=0.5[x₁(y₂-y₃)+x₂(y₃-y₁)+x₃(y₁-y₂)]

When the area of the triangle is zero then the given three points must be collinear.

Centroid of a Triangle

The point where all the three medians of the triangle meet with each other, is known as the centroid of a triangle

Centroid of a Triangle

The coordinates of the centroid are :

X=(X₁+X₂+X₃)/3, y=(y₁+y₂+y₃)/3

No.	Figures made of four points	Prove
1.	Square	Four sides are equal and the diagonals are also equal.
2.	Rhombus	Four sides are equal.
3.	Rhombus but not square	Four sides are equal and the diagonals are not equal.
4.	Rectangle	Opposite sides are equal and the diagonals are equal.
5.	Parallelogram	Opposite sides are equal.
6.	Parallelogram but not a rectangle	Opposite sides are equal but the diagonals are not equal.

No.	Figures made of three points	Prove
1.	Scalene triangle	None of its sides are equal.
2.	Isosceles triangle	Any two sides are equal.
3.	Equilateral triangle	All three sides are equal.
4.	Right triangle	The sum of the squares of any two sides is equal to the square of the third side.

Significance of NCERT Class 10 Maths Chapter 7 Notes

Coordinate Geometry Class 10 notes will help to understand the formulas, statements, rules in detail.

This NCERT Class 10 Maths chapter 7 notes also contains previous year’s questions and NCERT TextBook pdf. It contains FAQ’s or frequently asked questions along with the topic-wise explanation

In offline mode, Class 10 Maths chapter 7 notes pdf download can be used to prepare.

Class 10 Chapter Wise Notes

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NCERT Syllabus for Class 10

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Popular Questions

A block of mass 0.50 kg is moving with a speed of 2.00 ms^-1 on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is

Option 1) $0.34\; J$	Option 2) $0.16\; J$
Option 3) $1.00\; J$	Option 4) $0.67\; J$

A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1 m 1000 times. Assume that the potential energy lost each time he lowers the mass is dissipated. How much fat will he use up considering the work done only when the weight is lifted up ? Fat supplies 3.8×10⁷J of energy per kg which is converted to mechanical energy with a 20% efficiency rate. Take g = 9.8 ms⁻² :

Option 1)

2.45×10⁻³ kg

Option 2)

6.45×10⁻³ kg

Option 3)

9.89×10⁻³ kg

Option 4)

12.89×10⁻³ kg

An athlete in the olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range

Option 1) $2,000 \; J - 5,000\; J$	Option 2) $200 \, \, J - 500 \, \, J$
Option 3) $2\times 10^{5}J-3\times 10^{5}J$	Option 4) $20,000 \, \, J - 50,000 \, \, J$

A particle is projected at 60⁰ to the horizontal with a kinetic energy $K$ . The kinetic energy at the highest point

Option 1) $K/2\,$	Option 2) $\; K\;$
Option 3) $zero\;$	Option 4) $K/4$

In the reaction,

$2Al_{(s)}+6HCL_{(aq)}\rightarrow 2Al^{3+}\, _{(aq)}+6Cl^{-}\, _{(aq)}+3H_{2(g)}$

Option 1) $11.2\, L\, H_{2(g)}$ at STP is produced for every mole $HCL_{(aq)}$ consumed	Option 2) $6L\, HCl_{(aq)}$ is consumed for ever $3L\, H_{2(g)}$ produced
Option 3) $33.6 L\, H_{2(g)}$ is produced regardless of temperature and pressure for every mole Al that reacts	Option 4) $67.2\, L\, H_{2(g)}$ at STP is produced for every mole Al that reacts .

How many moles of magnesium phosphate, $Mg_{3}(PO_{4})_{2}$ will contain 0.25 mole of oxygen atoms?

Option 1) 0.02	Option 2) 3.125 × 10^-2
Option 3) 1.25 × 10^-2	Option 4) 2.5 × 10^-2

If we consider that 1/6, in place of 1/12, mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of a substance will

Option 1) decrease twice	Option 2) increase two fold
Option 3) remain unchanged	Option 4) be a function of the molecular mass of the substance.

With increase of temperature, which of these changes?

Option 1) Molality	Option 2) Weight fraction of solute
Option 3) Fraction of solute present in water	Option 4) Mole fraction.

Number of atoms in 558.5 gram Fe (at. wt.of Fe = 55.85 g mol^-1) is

Option 1) twice that in 60 g carbon	Option 2) 6.023 × 10²²
Option 3) half that in 8 g He	Option 4) 558.5 × 6.023 × 10²³

A pulley of radius 2 m is rotated about its axis by a force F = (20t - 5t²) newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg m² , the number of rotations made by the pulley before its direction of motion if reversed, is