Exercise 7.2 Class 10 Maths Ncert Solutions

NCERT solutions for class-10 maths chapter-7 Coordinate Geometry Exercise 7.2

NCERT Solutions for Class 10 Maths Chapter-7 Coordinate Geometry Exercise

NCERT solutions for class-10 maths Chapter-7 Coordinate Geometry Exercise is prepared by academic team of entrancei. These NCERT solutions will be updated according to the latest 2020-21 syllabus. We have prepared solutions for all exercises of this chapter. Given below is step by step solutions of all questions given in NCERT textbook for chapter-7. You have learned the formula of the given chapter. Entrancei prepared a detail notes and additional questions for class-10 maths with short notes of all maths formula of class-10 maths.

NCERT Solutions for Class 10 Maths Exercise 7.2


Solve the followings Questions.

1. Find the coordinates of the point which divides the join of (- 1, 7) and (4, - 3) in the ratio 2:3.

Answer:

Let P(x, y) be the required point. Using the section formula

chapter 7-Coordinate Geometry Exercise 7.2/18.PNG

chapter 7-Coordinate Geometry Exercise 7.2/18.PNG

Therefore the point is (1,3).

2. Find the coordinates of the points of trisection of the line segment joining (4, -1) and (-2, -3).

Answer:

chapter 7-Coordinate Geometry Exercise 7.2/18.PNG

Let P (x1,y1) and Q (x2,y2) are the points of trisection of the line segment joining the given points i.e., AP = PQ = QB

Therefore, point P divides AB internally in the ratio 1:2.

chapter 7-Coordinate Geometry Exercise 7.2/18.PNG

chapter 7-Coordinate Geometry Exercise 7.2/18.PNG

Therefore P(x1,y1) = (2, -5/3)

Point Q divides AB internally in the ratio 2:1.

chapter 7-Coordinate Geometry Exercise 7.2/18.PNG

chapter 7-Coordinate Geometry Exercise 7.2/18.PNG

Q (x2 ,y2) = (0, -7/3)

3. 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 the following figure. 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 flagexactly halfway between the line segment joining the two flags, where should she post her flag?

math 10

Answer:

It can be observed that Niharika posted the green flag at 1/4th of the distance AD i.e., (1×100/4)m = 25m from the starting point of 2nd line. Therefore, the coordinates of this point G is (2, 25).
Similarly, Preet posted red flag at 1/5 of the distance AD i.e., (1×100/5) m = 20m from the starting point of 8th line. Therefore, the coordinates of this point R are (8, 20).
Distance between these flags by using distance formula = GR
chapter 7-Coordinate Geometry Exercise 7.2/18.PNG
Therefore, Rashmi should post her blue flag at 22.5m on 5th line.


4. Find the ratio in which the line segment joining the points (-3, 10) and (6, - 8) is divided by (-1, 6).

Answer:
Let the ratio in which the line segment joining ( -3, 10) and (6, -8) is divided by point ( -1, 6) be k:1.
Therefore, -1 = 6k-3/k+1
-k - 1 = 6k -3
7k = 2
k = 2/7
Therefore, the required ratio is 2:7.


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.

Answer:
Let the ratio in which the line segment joining A (1, - 5) and B ( - 4, 5) is divided by x-axis be k:1.
Therefore, the coordinates of the point of division is (-4k+1/k+1, 5k-5/k+1).

We know that y-coordinate of any point on x-axis is 0.

∴ 5k-5/k+1 = 0

Therefore, x-axis divides it in the ratio 1:1.
chapter 7-Coordinate Geometry Exercise 7.2/19.PNG

6. If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, find x and y.

Answer:
chapter 7-Coordinate Geometry Exercise 7.2/fig-2.jpg

Let A,B,C and D be the points (1,2) (4,y), (x,6) and (3,5) respectively.

Mid point of diagonal AC ischapter 7-Coordinate Geometry Exercise 7.2/20.PNG

and Mid point of Diagonal BD ischapter 7-Coordinate Geometry Exercise 7.2/21.PNG

Since the diagonals of a parallelogram bisect each other, the mid point of AC and BD are same.

∴ x+1/2 = 7/2 and 4 = 5+y/2 ⇒ x + 1 = 7 and 5 + y = 8

⇒ x = 6 and y = 3

7. Find the coordinates of a point A, where AB is the diameter of circle whose centre is (2, - 3) and B is (1, 4).

Answer:

Let the coordinates of point A be (x, y).
Mid-point of AB is (2, - 3), which is the center of the circle.
chapter 7-Coordinate Geometry Exercise 7.2/22.PNG
⇒ x + 1 = 4 and y + 4 = -6

⇒ x = 3 and y = -10
Therefore, the coordinates of A are (3,-10).

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.

Answer:
chapter 7-Coordinate Geometry Exercise 7.2/fig-3.png

The coordinates of point A and B are (-2,-2) and (2,-4) respectively.

Since AP = 3/7 AB

Therefore, AP:PB = 3:4

Point P divides the line segment AB in the ratio 3:4.

chapter 7-Coordinate Geometry Exercise 7.2/23.PNG

9. Find the coordinates of the points which divide the line segment joining A (- 2, 2) and B (2, 8) into four equal parts.

Answer:
chapter 7-Coordinate Geometry Exercise 7.2/fig-4.PNG
From the figure, it can be observed that points X, Y, Z are dividing the line segment in a ratio 1:3, 1:1, 3:1 respectively.
chapter 7-Coordinate Geometry Exercise 7.2/24.PNG

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)]

Answer:
chapter 7-Coordinate Geometry Exercise 7.2/fig-5.PNG
Let (3, 0), (4, 5), ( - 1, 4) and ( - 2, - 1) are the vertices A, B, C, D of a rhombus ABCD.
chapter 7-Coordinate Geometry Exercise 7.2/25.PNG


Chapter-7 Coordinate Geometry Exercises


  1. Chapter-7 Coordinate Geometry Exercise-7.1

  2. Chapter-7 Coordinate Geometry Exercise-7.2

  3. Chapter-7 Coordinate Geometry Exercise-7.3

  4. Chapter-7 Coordinate Geometry Exercise-7.4

Exercise 7.2 Class 10 Maths Ncert Solutions

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