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

# 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.

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.

• 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

Distance formula

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

## 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

## 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 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

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

 NCERT Class 10 Maths Chapter 1 Notes NCERT Class 10 Maths Chapter 2 Notes NCERT Class 10 Maths Chapter 3 Notes NCERT Class 10 Maths Chapter 4 Notes NCERT Class 10 Maths Chapter 5 Notes NCERT Class 10 Maths Chapter 6 Notes NCERT Class 10 Maths Chapter 7 Notes NCERT Class 10 Maths Chapter 8 Notes NCERT Class 10 Maths Chapter 9 Notes NCERT Class 10 Maths Chapter 10 Notes NCERT Class 10 Maths Chapter 11 Notes NCERT Class 10 Maths Chapter 12 Notes NCERT Class 10 Maths Chapter 13 Notes NCERT Class 10 Maths Chapter 14 Notes NCERT Class 10 Maths Chapter 15 Notes

## NCERT Class 10 Exemplar Solutions for Other Subjects:

 NCERT Books for Class 10 NCERT Syllabus for Class 10

1. Find the area of the triangle ABC whose vertices are A(1, 2), B(4, 2), and C(3, 5).

Using the formula given above,

A = (1/2) [x1 (y2 – y3 ) + x2 (y3 – y1 ) + x3(y1 – y2)] A = (1/2) [1(2 – 5) + 4(5 – 2) + 3(2 – 2)] A = (1/2) [-3 + 12]

Area = 9/2 square units. Therefore, the area of a triangle ABC is 9/2 square units.

2. Find the ratio when point (– 4, 6) divide the line segment joining the points A(– 6, 10) and B(3, – 8)?

Using the formula given above,

A = (1/2) [x1 (y2 – y3 ) + x2 (y3 – y1 ) + x3(y1 – y2)] A = (1/2) [1(2 – 5) + 4(5 – 2) + 3(2 – 2)] A = (1/2) [-3 + 12]

Area = 9/2 square units. Therefore, the area of a triangle ABC is 9/2 square units.

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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

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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 3.8×107 J 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

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

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In the reaction,

 Option 1)   at STP  is produced for every mole   consumed Option 2)   is consumed for ever      produced Option 3) is produced regardless of temperature and pressure for every mole Al that reacts Option 4) at STP is produced for every mole Al that reacts .

How many moles of magnesium phosphate, 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.

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

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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

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