Teach on Udemy

Turn what you know into an opportunity and reach millions around the world.

Learn More

Your cart is empty.

Keep shopping

Mastering Analytical Geometry

Name: Mastering Analytical Geometry
Rating: 4.5 (1 reviews)

High school math that covers Two Dimensional Geometry in detail - Unlocking the Power of Coordinate Geometry.

Created byLakshmi Narayana

Last updated 6/2023

English

What you'll learn

Review of Concepts of Coordinate Geometry: Cartesian System, Coordinates of a point in Cartesian plane, and Quadrants.
Distance Formula and its applications.
Section Formula and its applications.
Mid-Point Formula & Centroid of Triangle
Area of a Triangle & Collinearity
Applications of Coordinate Geometry in real life.
At the end of the course, students will not only have learned about the topics in detail but also be able to solve various problems based on them.

Course content

11 sections • 70 lectures • 10h 2m total length

Introduction12:03
Introduction:
Q 13:31
Find the distance of :
1) The point P (2, 3) from the x-axis.
2) The point (4, 7) from the y-axis.
Q 22:33
Find the coordinates of the point, where the line x - y = 5 cuts Y - axis.
Q 32:35
If P is a point on x-axis such that its distance from the origin is 3 units, then the coordinates of a point Q on OY such that OP = OQ, are ?

1. (0, 0)
2. (3, 0)
3. (0, -3)
4. (0, 3)
Q 45:23
Find the coordinates of the vertices of an equilateral triangle of side 2a.
Test your understanding
Home Assignment

Introduction6:26
Distance Formula & its applications.
Q 12:21
Find the distance between the
points A (0, 6) and B (0, –2).
Q 21:43
Find the distance of the point P(–6, 8) from the origin.
Q 35:29
Find a relation between x and y such that the point
(x, y) is equidistant from the points (7, 1) and (3, 5).
Q 46:49
Find the points of X-axis which are at a distance of 2 from the point (7, −4). How many such points are there?
Q 56:08
Find a point on the y−axis which is equidistant
from the points A (6, 5) and B (– 4, 3).
Test your understanding
Home Assignment

Introduction4:33
Distance Formula & its applications
Q 19:41
Do the points (3, 2), (–2, –3) and (2, 3) form a triangle?
If so, name the type of triangle formed.
Q 29:18
Show that the points (1, 7), (4, 2), (–1, –1)
and (– 4, 4) are the vertices of a square.
Q 36:10
Figure shows the arrangement of desks in a classroom. Ashima, Bharti and Camella are seated at A(3, 1), B(6, 4) and C(8, 6) respectively. Do you think they are seated in a line? Give reasons for your answer.
Q 46:51
Prove that the points (a, b + c), (b, c + a)
and (c, a + b) are collinear.
Test your understanding
Home Assignment

Introduction10:39
Section Formula & mid-point formula
Q 13:56
Find the coordinates of the point which divides the line segment joining the points (4, – 3) and (8, 5) in the ratio 3 : 1 internally.
Q 26:41
In what ratio does the point (– 4, 6) divide the line
segment joining the points A (– 6, 10) and B (3, – 8)?
Q 37:28
Determine the ratio in which the point P (m, 6) divides
the join of A(–4, 3) and B(2, 8). Also find the value of m.
Q 44:04
Find the coordinates of a point A, where AB is the diameter
of a circle whose centre is (2, -3) and B is (1, 4).
Test your understanding
Home Assignment

Introduction3:39
Section Formula
Mid-point
Centroid formula
points of trisection
Q 15:53
Find the coordinates of the points of trisection (i.e., points dividing in three equal parts) of the line segment joining the points A (2, – 2) and B (– 7, 4).
Q 27:45
Find the ratio in which the y-axis divides the line segment joining the points (5, – 6) and (–1, – 4). Also find the point of intersection.
Q 34:20
If the points A (6, 1), B (8, 2), C (9, 4) and D (p, 3) are the vertices of a parallelogram, taken in order, find the value of p.
Q 45:24
If the point C (–1, 2) divides internally the line segment joining the points A (2, 5) and B(x, y) in the ratio 3 : 4, find the value of x2 + y2.
Test your understanding
Home Assignment

Introduction7:21
Area of a Triangle & its applications.
Q 13:39
Find the area of a triangle whose vertices are
(1, –1), (– 4, 6) and (–3, –5).
Q 23:40
Find the area of a triangle formed by the points
A (5, 2), B (4, 7) and C (7, – 4).
Q 33:26
Find the area of the triangle formed by the points
P(–1.5, 3), Q (6, –2) and R (–3, 4).
Q 48:06
If A (–5, 7), B (– 4, –5), C (–1, –6) and D (4, 5) are the vertices
of a quadrilateral, find the area of the quadrilateral ABCD.
Test your understanding
Home Assignment

Introduction2:07
Area of a Triangle & Collinearity
of Three points
Method to Find the Unknown when Three points are Collinear
Q 12:36
Show that the points A (0, 1), B (2, 3) and C (3, 4) are collinear.
Q 23:01
Check whether the points (0, 5), (0, –9) and (3, 6) are collinear.
Q 33:21
If the points A(1, 2), O(0, 0) and C(a, b) are collinear, then
(A) a = b (B) a = 2b (C) 2a = b (D) a = –b
Q 43:35
Find the value of k if the points A (2, 3),
B (4, k) and C(6, –3) are collinear.
Q 54:05
If (5, 2), (− 3, 4) and (x, y) are collinear,
show that x + 4y − 13 = 0.
Test your understanding
Home Assignment

Q 110:46
Find the distance between the
following pairs of points:
(i) (2, 3), (4, 1)
(ii) (–5, 7), (–1, 3)
(iii) (a, b), (–a, –b)
Q 25:36
Find the distance between the points (0, 0) and (36, 15). Also, find the distance between towns A and B if town B is located at 36km east and 15km north of town A.
Q 39:33
Determine if the points (1, 5), (2, 3) and (–2, –11) are collinear.
Q 47:20
Check whether (5, –2), (6, 4) and (7, –2) are
the vertices of an isosceles triangle.
Q 515:45
In a classroom, 4 friends are seated at the points A, B, C and Das shown in figure. Champa and Chameli walk into the class and after observing for a few minutes Champa asks Chameli. "Don't you think ABCD is a square?"Chameli disagrees. Using distance formula, find which of them is correct.
Q 642:29
Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer:
(i) (–1, –2), (1, 0), (–1, 2), (–3, 0)
(ii) (–3, 5), (3, 1), (0, 3), (–1, –4)
(iii) (4, 5), (7, 6), (4, 3), (1, 2)
Q 711:24
Find the point on the x–axis which is equidistant
from (2, –5) and (–2, 9)
Q 88:19
Find the values of y for which the distance between
the points P (2, –3) and Q (10, y) is 10 units.
Q 913:26
If, Q (0, 1) is equidistant from P (5, –3) and R (x, 6), find the values of x. Also, find the distances QR and PR.
Q 109:09
Find a relation between x and y such that the point (x, y) is equidistant from the point (3, 6) and (–3, 4).

Q 15:06
Find the coordinates of the point which divides the line segment join of (–1, 7) and (4, –3) in the ratio 2:3.
Q 210:35
Find the coordinates of the points of trisection of the line segment joining (4, –1) and (–2, –3).
Q 312:47
To conduct sports day activities, in your rectangular shaped school ground ABCD, lines have been drawn with chalk powder at a distance of 1 m each. 100 flower pots have been placed at a distance of 1 m from each other along AD as shown in figure. Niharika runs 1/4 of the distance AD on the 2nd line and posts a green flag. Preet runs 1/5of the distance AD on the eighth line and posts a red flag. What is the distance between both the flags? If Rashmi has to post a blue flag exactly halfway between the line segment joining the two flags, where should she post her flag?
Q 46:48
Find the ratio in which the line segment joining the points (–3, 10) and (6, –8) is divided by (–1, 6).
Q 59:31
Find the ratio in which the line segment joining A (1, –5) and B(–4, 5) is divided by the x–axis. Also find the coordinates of the point of division.
Q 67:38
If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, find x and y.
Q 77:11
Find the coordinates of a point A, where AB is the diameter of a circle whose centre is (2, –3) and B is (1, 4).
Q 86:06
If A and B are (–2, –2) and (2, –4) respectively, find the coordinates of P such that AP = 3/7 A B and P lies on the line segment AB.
Q 911:40
Find the coordinates of the points which divides the line segment joining A (–2, 2) and B (2, 8) into four equal parts.
Q 107:35
Find the area of a rhombus if its vertices are (3, 0),
(4, 5), (–1, 4) and (–2, –1) taken in order.
[Hint: Area of a rhombus = 1/2(product of its diagonals)]

Q 18:18
Find the area of the triangle whose vertices are:
(i)(2,3),(–1,0),(2,–4)
(ii) (–5, –1), (3, –5), (5,2)
Q 28:55
Ineachofthefollowingfindthevalueof'k',forwhichthepointsarecollinear.
(i)(7,–2),(5,1),(3,k)
(ii) (8, 1), (k, –4), (2,–5)
Q 314:04
Find the area of the triangle formed by joining the mid–points of the sides of the trianglewhoseverticesare(0,–1),(2,1)and(0,3).Findtheratioofthisareatothearea of the giventriangle.
Q 49:36
Find the area of the quadrilateral whose vertices taken in order are (–4, –2), (–3,–5), (3, –2) and (2,3).
Q 512:05
We know that median of a triangle divides it into two triangles of equal areas. Verify this result for △ABC whose vertices are A (4,–6),B(3,–2) and C(5,2).

Requirements

Elementary knowledge of basic fundamental operations - Addition, Subtraction, Product, and Ratio.
Elementary knowledge of middle school math.
Each chapter is inbuilt with prerequisite knowledge classes where the child gets immense knowledge and a clear understanding of the chapters.

Description

This course is intended for underage students. The course can only be purchased by parents, and students must watch under the supervision of an adult parent. This course is carefully designed to explain various topics in Two Dimensional Geometry - Coordinate Geometry .

It has 71 lectures spanning ten hours of on-demand videos that are divided into 7 sessions. The course is divided into a simplified day-by-day learning schedule.
Each topic is divided into simple sessions and explained extensively by solving multiple questions. Each session contains a detailed explanation of the concept.
An online test related to the concept for immediate assessment of understanding.
Session-based daily home assignments with a separate key The students are encouraged to solve practice questions and quizzes provided at the end of each session.
This course will give you a firm understanding of the fundamentals and is designed in a way that a person with little or no previous knowledge can also understand very well.
It covers 100% video solutions of the NCERT exercises , with selected NCERT exemplars and R D Sharma.
Our design meets the real classroom experience by following classroom teaching practices. We have designed this course by keeping in mind all the needs of students and their desire to become masters in math. This course is designed to benefit all levels of learners and will be the best gift for board-appearing students. Students love these easy methods and explanations. They enjoy learning maths and never feel that maths is troublesome.

Topics covered in the course:

Review of Concepts of Coordinate Geometry
- Cartesian System
- Coordinates of a point in Cartesian plane
- Quadrants
Distance Formula
Section Formula
Mid-Point Formula
Centroid of Triangle
Area of a Triangle & Collinearity
Applications of Coordinate Geometry in real life.

With this course you'll also get:

Perfect your mathematical skills on Two Dimensional Geometry.
A Udemy Certificate of Completion is available for download.

Feel free to contact me with any questions or clarifications you might have.

I can't wait for you to get started on mastering the real number systems.

I look forward to seeing you on the course! :)

Benefits of Taking this Course:

On completion of this course, one will have detailed knowledge of the chapter and be able to easily solve all the problems, which can lead to scoring well in exams with the help of explanatory videos ensure complete concept understanding.

Downloadable resources help in applying your knowledge to solve various problems.

Quizzes help in testing your knowledge. In short, one can excel in math by taking this course.

Who this course is for:

This course has been designed for students of the Grade 10th CBSE, ICSE, SSC, GCSE, IGCSE, SAT, ACT, GRE, and other board-appearing students.
Students studying for the public or other competitive examinations
Home-school parents are looking for extra support with the fundamentals.
Anyone interested in revising or learning the basics of mathematics should.
Students in junior high and high school/secondary schools.
Anyone who wants to proficient mathematics and the Coordinate Geometry(2D Geometry) well.
Anyone who wants to study math for fun after taking a break from school.
It will also benefit schools who wish to run classes in the absence of a teacher and make learning fun for their students.
It will also benefit teachers and schools who wish to improve their teaching skills and make learning fun for their students.
For 11th, 9th, and 8th grade students, this will help as a bridge course.

Mastering Analytical Geometry

What you'll learn

Explore related topics

Course content

Session-15 lectures • 26min

Session-26 lectures • 29min

Session-35 lectures • 37min

Session-45 lectures • 33min

Session-55 lectures • 27min

Session-65 lectures • 26min

Session-76 lectures • 19min

Exercise 7.110 lectures • 2hr 14min

Exercise 7.210 lectures • 1hr 25min

Exercise 7.35 lectures • 53min

Requirements

Description

Who this course is for: