Coordinate Geometry | Complete NCERT WITH BACK EXERCISE in 1 Video | Class 10th Board

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00:00 - Introduction
02:38 - Exercise - 7.1
01:05:05 - Exercise - 7.2
01:59:13 - Thank You !

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[Arnav_]

13:15-
The distance between the two points can be measured using the Distance Formula which is given by: Distance Formula = √ [(x₂ - x₁)2 + (y₂ - y₁)2]

Let the points be A(0, 0) and B(36, 15)

Hence, x₁ = 0, y₁ = 0, x₂ = 36, y₂ = 15

We know that the distance between the two points is given by the Distance Formula,

= √ [(x₂ - x₁)2 + (y₂ - y₁)2]....(1)

= √ (36 - 0)2 + 15 - 0)2

= √ [(1296) + (225)]

= √1521

= 39

Yes, it is possible to find the distance between the given towns A and B.

The positions of towns A & B are given by (0, 0) and (36, 15), hence, as calculated above, the distance between town A and B will be 39 km.

38:57 -
ii) Let A (- 3, 5), B (3, 1), C (0, 3), and D (- 1, - 4) be the four points of the quadrilateral.

We know that the distance between any two points is given by the distance formula = √(x₁ - x₂)² + (y₁ - y₂)²

To find AB, that is, the distance between points A (- 3, 5) and B (3, 1) by using the distance formula,

AB = √(3 + 3)² + (1 - 5)²

= √(6)² + (- 4)²

= √36 + 16

= √52

= 2√13 units

To find BC, that is, distance between points B (3, 1) and C (0, 3) by using the distance formula,

BC = √(0 - 3)² + (3 - 1)²

= √ (-3)² + (2)²

= √9 + 4

= √13 units

To find CD, that is, distance between Points C (0, 3), and D (- 1, - 4) by using the distance formula,

CD = √(- 1 - 0)² + (- 4 - 3)²

= √ (- 1)² + (- 7)²

= √1 + 49

= √50

= 5√2 units

To find AD, that is, distance between Points A (- 3, 5) and D (- 1, - 4) using distance formula,

AD = √(-1 + 3)² + (- 4 - 5)²

= √ (2)² + (- 9)²

= √4 + 81

= √85 units

Since, AB ≠ BC ≠ CD ≠ AD, therefore, no special quadrilateral can be formed from the given vertices.

iii) Let A (4, 5), B (7, 6), C (4, 3) and D (1, 2) be the four points of the quadrilateral.

We know that the distance between any two points is given by the Distance Formula,

Distance Formula = √ (x₁ - x₂)² + (y₁ - y₂)²

To find AB, that is, distance between points A (4, 5) and B (7, 6), by using the distance formula,

AB = √(7 - 4)² + (6 - 5)²

= √3² + 1²

= √9 + 1

= √10 units

To find BC, that is, distance between points B (7, 6) and C (4, 3) by using the distance formula,

BC = √ (4 - 7 )² + (3 - 6)²

= √ (- 3)² + 3²

= √9 + 9

= √18 units

To find CD, that is, distance between points C (4, 3) and D (1, 2) by using the distance formula,

CD = √(1 - 4)² + (2 - 3)²

= √ (- 3)² + (- 1)²

= √9 + 1

= √10 units

To find AD i.e. Distance between points A (4, 5) and D (1, 2) using distance formula,

AD = √( 1 - 4 )² + ( 2 - 5)²

= √ (- 3)² + (- 3)²

= √ 9 + 9

= √18 units

To find AC, the distance between points A (4, 5) and C (4, 3), we have

Diagonal AC = √( 4 - 4 )² + ( 3 - 5)²

= √( 0 )² + ( - 2)²

= 2 units

To find BD, distance between points B (7, 6) and D (1, 2), we have

Diagonal BD = √(1 - 7)² + (2 - 6)²

= √ ( - 6 )² + ( - 4 )²

= √ 36 + 16

= √52 units

Since AB = CD and BC = AD, but the diagonals AC ≠ BD, thus the quadrilateral is a parallellogram.

1:21:32 -
P, Q, R divides the line segment A (- 2, 2) and B (2, 8) into four equal parts.

Point P divides the line segment AQ into two equal parts.

Therefore, AP : PB is 1 : 3

Using section formula which is given by P (x, y) = [(mx₂ + nx₁) / m + n, (my₂ + ny₁) / m + n]

Hence, coordinates of P = [(1 × 2 + 3 × (- 2)) / (3 + 1), (1 × 8 + 3 × 2) / (3 + 1)] = (- 1, 7/2)

Point Q divides the line segment AB into two equal parts

Using mid point formula,

Q = [(2 + (- 2)) / 2, (2 + 8) / 2] = (0, 5)

Point R divides the line segment BQ into two equal parts

Coordinates of R = [(2 + 0) / 2, (8 + 5) / 2] = (1, 13/2)

1:58:24-
A rhombus has all sides of equal length and opposite sides are parallel.

Let A(3, 0), B(4, 5), C(- 1, 4) and D(- 2, - 1) be the vertices of a rhombus ABCD.

Also, Area of a rhombus =1/2 × (product of its diagonals)

Hence we will calculate the values of the diagonals AC and BD.

We know that the distance between the two points is given by the distance formula,

Distance formula = √( x₂ - x₁ )2 + (y₂ - y₁)2

Therefore, distance between A (3, 0) and C (- 1, 4) is given by

Length of diagonal AC =√ [3 - (-1)]2 + [0 - 4]2

= √(16 + 16)

= 4√2

The distance between B (4, 5) and D (- 2, - 1) is given by

Length of diagonal BD = √[4 - (-2)]2 + [5 - (-1)]2

= √(36 + 36)

= 6√2

Area of the rhombus ABCD = 1/2 × (Product of lengths of diagonals) = 1/2 × AC × BD

Therefore, the area of the rhombus ABCD = 1/2 × 4√2 × 6√2 square units

= 24 square units

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[HardikModi_]

00:01 Coordinate Geometry and NCERT back exercises discussed in the video
01:57 Coordinate geometry is a scoring chapter with easy concepts but requires careful calculations.
06:20 Understanding coordinate geometry concepts and distance formula
08:29 Summary of Coordinate Geometry concepts and formulas
13:02 Understanding the concept of collinear points
15:03 Coordinate Geometry and Collinearity
20:14 Explaining how to determine if three points are collinear or form an isosceles triangle
22:52 Using operations with coordinate geometry
27:30 Understanding the concept of a square in geometry
29:46 Understanding the concept of squares in coordinate geometry
33:58 Understanding and applying the distance formula
36:07 Understanding coordinate geometry concepts and calculations
40:18 Understanding coordinates and distance from x-axis
42:11 Understanding distance from x and y axis
46:56 Explaining the process of squaring and removing under roots
48:58 Finding a point with equal distance from two given points on the x-axis
53:22 Key points on solving equations in Coordinate Geometry
56:06 Summarizing coordinate geometry concepts for Class 10th Board
1:00:59 Solving equations using coordinate geometry
1:03:32 Understanding section formula for finding coordinates of a point
1:07:53 Section formula helps find coordinates of a point dividing a line segment
1:10:04 Finding coordinates of a point which divides a line segment
1:14:46 Introduction to Coordinate Geometry concepts.
1:16:45 Explaining how to find coordinates using formulas
1:21:19 Understanding the concept of mid point formula
1:23:21 Explaining the section formula and midpoint formula
1:27:57 Understanding and calculating coordinates of flags and distance formula
1:30:36 Understanding coordinates and midpoint in geometry
1:35:06 Understanding the division ratio of a line segment
1:37:19 Understanding the division of line segments on the x-axis
1:41:39 Understanding the concept of Taken in Order
1:43:54 Understanding of midpoints and diagonals in coordinate geometry
1:48:16 Finding the center and coordinates of a circle
1:50:31 Understanding the mid point formula and its application.
1:55:03 Understanding and finding coordinates using ratios
1:57:21 Formula for Area of Rhombus requires halving product of diagonals

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[tejaschhokar]

The distance between the two points can be measured using the Distance Formula which is given by: Distance Formula = √ [(x₂ - x₁)2 + (y₂ - y₁)2]

Let the points be A(0, 0) and B(36, 15)

Hence, x₁ = 0, y₁ = 0, x₂ = 36, y₂ = 15

We know that the distance between the two points is given by the Distance Formula,

= √ [(x₂ - x₁)2 + (y₂ - y₁)2]....(1)

= √ (36 - 0)2 + 15 - 0)2

= √ [(1296) + (225)]

= √1521

= 39

Yes, it is possible to find the distance between the given towns A and B.

The positions of towns A & B are given by (0, 0) and (36, 15), hence, as calculated above, the distance between town A and B will be 39 km.

38:57 -
ii) Let A (- 3, 5), B (3, 1), C (0, 3), and D (- 1, - 4) be the four points of the quadrilateral.

We know that the distance between any two points is given by the distance formula = √(x₁ - x₂)² + (y₁ - y₂)²

To find AB, that is, the distance between points A (- 3, 5) and B (3, 1) by using the distance formula,

AB = √(3 + 3)² + (1 - 5)²

= √(6)² + (- 4)²

= √36 + 16

= √52

= 2√13 units

To find BC, that is, distance between points B (3, 1) and C (0, 3) by using the distance formula,

BC = √(0 - 3)² + (3 - 1)²

= √ (-3)² + (2)²

= √9 + 4

= √13 units

To find CD, that is, distance between Points C (0, 3), and D (- 1, - 4) by using the distance formula,

CD = √(- 1 - 0)² + (- 4 - 3)²

= √ (- 1)² + (- 7)²

= √1 + 49

= √50

= 5√2 units

To find AD, that is, distance between Points A (- 3, 5) and D (- 1, - 4) using distance formula,

AD = √(-1 + 3)² + (- 4 - 5)²

= √ (2)² + (- 9)²

= √4 + 81

= √85 units

Since, AB ≠ BC ≠ CD ≠ AD, therefore, no special quadrilateral can be formed from the given vertices.

iii) Let A (4, 5), B (7, 6), C (4, 3) and D (1, 2) be the four points of the quadrilateral.

We know that the distance between any two points is given by the Distance Formula,

Distance Formula = √ (x₁ - x₂)² + (y₁ - y₂)²

To find AB, that is, distance between points A (4, 5) and B (7, 6), by using the distance formula,

AB = √(7 - 4)² + (6 - 5)²

= √3² + 1²

= √9 + 1

= √10 units

To find BC, that is, distance between points B (7, 6) and C (4, 3) by using the distance formula,

BC = √ (4 - 7 )² + (3 - 6)²

= √ (- 3)² + 3²

= √9 + 9

= √18 units

To find CD, that is, distance between points C (4, 3) and D (1, 2) by using the distance formula,

CD = √(1 - 4)² + (2 - 3)²

= √ (- 3)² + (- 1)²

= √9 + 1

= √10 units

To find AD i.e. Distance between points A (4, 5) and D (1, 2) using distance formula,

AD = √( 1 - 4 )² + ( 2 - 5)²

= √ (- 3)² + (- 3)²

= √ 9 + 9

= √18 units

To find AC, the distance between points A (4, 5) and C (4, 3), we have

Diagonal AC = √( 4 - 4 )² + ( 3 - 5)²

= √( 0 )² + ( - 2)²

= 2 units

To find BD, distance between points B (7, 6) and D (1, 2), we have

Diagonal BD = √(1 - 7)² + (2 - 6)²

= √ ( - 6 )² + ( - 4 )²

= √ 36 + 16

= √52 units

Since AB = CD and BC = AD, but the diagonals AC ≠ BD, thus the quadrilateral is a parallellogram.

1:21:32 -
P, Q, R divides the line segment A (- 2, 2) and B (2, 8) into four equal parts.

Point P divides the line segment AQ into two equal parts.

Therefore, AP : PB is 1 : 3

Using section formula which is given by P (x, y) = [(mx₂ + nx₁) / m + n, (my₂ + ny₁) / m + n]

Hence, coordinates of P = [(1 × 2 + 3 × (- 2)) / (3 + 1), (1 × 8 + 3 × 2) / (3 + 1)] = (- 1, 7/2)

Point Q divides the line segment AB into two equal parts

Using mid point formula,

Q = [(2 + (- 2)) / 2, (2 + 8) / 2] = (0, 5)

Point R divides the line segment BQ into two equal parts

Coordinates of R = [(2 + 0) / 2, (8 + 5) / 2] = (1, 13/2)

1:58:24-
A rhombus has all sides of equal length and opposite sides are parallel.

Let A(3, 0), B(4, 5), C(- 1, 4) and D(- 2, - 1) be the vertices of a rhombus ABCD.

Also, Area of a rhombus =1/2 × (product of its diagonals)

Hence we will calculate the values of the diagonals AC and BD.

We know that the distance between the two points is given by the distance formula,

Distance formula = √( x₂ - x₁ )2 + (y₂ - y₁)2

Therefore, distance between A (3, 0) and C (- 1, 4) is given by

Length of diagonal AC =√ [3 - (-1)]2 + [0 - 4]2

= √(16 + 16)

= 4√2

The distance between B (4, 5) and D (- 2, - 1) is given by

Length of diagonal BD = √[4 - (-2)]2 + [5 - (-1)]2

= √(36 + 36)

= 6√2

Area of the rhombus ABCD = 1/2 × (Product of lengths of diagonals) = 1/2 × AC × BD

Therefore, the area of the rhombus ABCD = 1/2 × 4√2 × 6√2 square units

= 24 square units

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[_MaryamFareed]

1:21:26
Point (p) coordinates
(-1, 7/2)
Point Q coordinates
(0, 5)
And point R coordinates
(1, 13/2)

[PinkiKumari-jr]

The answer of question 6th of part (ii) is No any quadrilateral and (iii) is Parallelogram.

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[Annie_hubs]

39:31 answer (ii) no quadrilateral (iii) parallelogram