# 7. Coordinate Geometry

##### 5 LECTURES

• This page has links to complete syllabus of NCERT Chapter 7 Coordinate Geometry based on syllabus recommended by CBSE based on class 10 maths.
• There are 4 video lectures having explanations from basic to advance concepts, each and every NCERT solutions, questions and all important examples. You can access them directly from the lecture menu or just scroll down the page.
• All lecture were uploaded on YouTube so for better learning experience here you will find link to YouTube Playlist of Chapter 7 Coordinate Geometry.
• Also, there are detailed highlights of each video lecture with exact timestamp links so that you can easily access all topics and questions directly.
• Just click on the timestamp link and you will be redirected to video watch page at exactly that time.
• You can ask doubts in Coordinate Geometry at the end of this page.

##### 7(A) || Exercise 7.1 (Q1 to Q5) Distance Formula

00:00:20 Meaning and use of Coordinate Geometry

00:04:00 Derivation of Distance Formula (Finding distance between two points)

00:16:40 NCERT Exercise 7.1 Questions 1 Find the distance between the following pairs of points : (i) (2, 3), (4, 1) (ii) (– 5, 7), (– 1, 3) (iii) (a, b), (– a, – b)

00:22:00 NCERT Exercise 7.1 Questions 2 Find the distance between the points (0, 0) and (36, 15). Can you now find the distance between the two towns A and B discussed in Section 7.2.

00:24:50 NCERT Exercise 7.1 Questions 3 (Collinear points using Distance formula) Determine if the points (1, 5), (2, 3) and (– 2, – 11) are collinear.

00:34:50 NCERT Exercise 7.1 Questions 4 Check whether (5, – 2), (6, 4) and (7, – 2) are the vertices of an isosceles triangle.

00:40:00 NCERT Exercise 7.1 Questions 5 In a classroom, 4 friends are seated at the points A, B, C and D as shown in Fig. 7.8. 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.

##### 7(B) || Exercise 7.1 (Q6 to Q10)

00:00:20 Basic differences between Square, Rhombus, Rectangle and Parallelogram

00:02:35 NCERT Exercise 7.1 Questions 6 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)

00:15:45 NCERT Exercise 7.1 Questions 7 Find the point on the x-axis which is equidistant from (2, –5) and (–2, 9).

00:21:35 NCERT Exercise 7.1 Questions 8 Find the values of y for which the distance between the points P(2, – 3) and Q(10, y) is 10 units.

00:27:36 NCERT Exercise 7.1 Questions 9 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.

00:32:35 NCERT Exercise 7.1 Questions 10 Find a relation between x and y such that the point (x, y) is equidistant from the point (3, 6) and (– 3, 4).

##### 7(C) || Section Formula Exercise 7.2

00:00:20 Derivation of Section Formula

00:13:03 NCERT Exercise 7.2 Questions 1 Find the coordinates of the point which divides the join of (–1, 7) and (4, –3) in the ratio 2 : 3.

00:15:13 NCERT Exercise 7.2 Questions 2 Find the coordinates of the points of trisection of the line segment joining (4, –1) and (–2, –3).

00:21:22 Derivation of Mid-point formula

00:29:13 NCERT Exercise 7.2 Questions 3 To conduct Sports Day activities, in your rectangular shaped school ground ABCD, lines have been drawn with chalk powder at a distance of 1m each. 100 flower pots have been placed at a distance of 1m from each other along AD, as shown in Fig. 7.12. Niharika runs 1/4th the distance AD on the 2nd line and posts a green flag. Preet runs 1/5th 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?

00:35:33 NCERT Exercise 7.2 Questions 8 If A and B are (– 2, – 2) and (2, – 4), respectively, find the coordinates of P such that AP = 3/7 AB and P lies on the line segment AB.

00:38:53 NCERT Exercise 7.2 Questions 7 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).

00:45:23 NCERT Exercise 7.2 Questions 6 If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, find x and y.

##### 7(D) || Area of Triangle Exercise 7.2 Exercise 7.3

00:00:20 NCERT Exercise 7.2 Questions 4 Find the ratio in which the line segment joining the points (– 3, 10) and (6, – 8) is divided by (– 1, 6).

00:09:30 NCERT Exercise 7.2 Questions 5 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.

00:16:50 NCERT Exercise 7.2 Questions 9 Find the coordinates of the points which divide the line segment joining A(– 2, 2) and B(2, 8) into four equal parts.

00:22:20 NCERT Exercise 7.2 Questions 10 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)]

00:28:10 Area of triangle using coordinates of vertices

00:30:30 NCERT Exercise 7.3 Questions 1 Find the area of the triangle whose vertices are : (i) (2, 3), (–1, 0), (2, – 4) (ii) (–5, –1), (3, –5), (5, 2)

00:34:30 Proving points are collinear using area of triangle

00:37:00 NCERT Exercise 7.3 Questions 2 In each of the following find the value of ‘k’, for which the points are collinear. (i) (7, –2), (5, 1), (3, k) (ii) (8, 1), (k, – 4), (2, –5)

00:42:00 NCERT Exercise 7.3 Questions 3 Find the area of the triangle formed by joining the mid-points of the sides of the triangle whose vertices are (0, –1), (2, 1) and (0, 3). Find the ratio of this area to the area of the given triangle.

00:49:00 NCERT Exercise 7.3 Questions 4 Find the area of the quadrilateral whose vertices, taken in order, are (– 4, – 2), (– 3, – 5), (3, – 2) and (2, 3).

00:54:50 NCERT Exercise 7.3 Questions 5 You have studied in Class IX, (Chapter 9, Example 3), that a 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).