RD Sharma Solutions for Class 10 Chapter 14 Co-ordinate Geometry Exercise 14.4

Applications of section formula comprise the main subject in this exercise. Students will understand how to find the coordinates of the centroid of a triangle as an application of section formula. The RD Sharma Solutions Class 10 can be used as a quick reference for solutions to problems in any chapter of the book. Students can also download the RD Sharma Solutions for Class 10 Maths Chapter 14 Co-ordinate Geometry Exercise 14.4 PDF, which is provided below.

RD Sharma Solutions for Class 10 Chapter 14 Co-ordinate Geometry Exercise 14.4 Download PDF

 

rd sharma solutions class 10 chapter 14 exercise 4
rd sharma solutions class 10 chapter 14 exercise 4
rd sharma solutions class 10 chapter 14 exercise 4

 

Access RD Sharma Solutions for Class 10 Chapter 14 Co-ordinate Geometry Exercise 14.4

1. Find the centroid of the triangle whose vertices are:

(i) (1, 4), ( -1, -1) and (3, -2) (ii) (-2, 3), (2, -1) and (4, 0)

Solution:

We know that the coordinates of the centroid of a triangle whose vertices are

(x1, y1), (x2, y2), (x3, y3) are

R D Sharma Solutions For Class 10 Maths Chapter 14 Co-ordiniate Geometry ex 14.4 - 1

(i) So, the coordinates of the centroid of a triangle whose vertices are

(1, 4), (-1, -1) and (3, -2) are

R D Sharma Solutions For Class 10 Maths Chapter 14 Co-ordiniate Geometry ex 14.4 - 2

(1, 1/3)

Thus, centroid of the triangle is (1, 1/3)

(ii) So, the coordinates of the centroid of a triangle whose vertices are

(-2, 3), (2, -1) and (4, 0) are

R D Sharma Solutions For Class 10 Maths Chapter 14 Co-ordiniate Geometry ex 14.4 - 3

(4/3, 2/3)

Thus, centroid of the triangle is (4/3, 2/3)

 

2. Two vertices of a triangle are (1, 2), (3, 5) and its centroid is at the origin. Find the coordinates of the third vertex.

Solution:

Let the coordinates of the third vertex be (x, y)

Then, we know that the coordinates of centroid of the triangle are

R D Sharma Solutions For Class 10 Maths Chapter 14 Co-ordiniate Geometry ex 14.4 - 4

Given that the centroid for the triangle is at the origin (0, 0)

R D Sharma Solutions For Class 10 Maths Chapter 14 Co-ordiniate Geometry ex 14.4 - 5

⇒ x + 4 = 0 ⇒ y + 7 = 0

⇒ x = -4 ⇒ y = -7

Therefore, the coordinates of the third vertex is (-4, -7)

3. Find the third vertex of a triangle, if two of its vertices are at (-3, 1) and (0, -2) and the centroid is at the origin.

Solution:

Let the coordinates of the third vertex be (x, y)

Then, we know that the coordinates of centroid of the triangle are

R D Sharma Solutions For Class 10 Maths Chapter 14 Co-ordiniate Geometry ex 14.4 - 6

Given that the centroid for the triangle is at the origin (0, 0)

R D Sharma Solutions For Class 10 Maths Chapter 14 Co-ordiniate Geometry ex 14.4 - 7

⇒ x – 3 = 0 ⇒ y – 1 = 0

⇒ x = 3 ⇒ y = 1

Therefore, the coordinates of the third vertex is (3, 1)

4. A(3, 2) and B(-2, 1) are two vertices of a triangle ABC whose centroid G has the coordinates (5/3, -1/3). Find the coordinates of the third vertex C of the triangle.

Solution:

Let the coordinates of the third vertex C be (x, y)

Given, A(3, 2) and B(-2, 1) are two vertices of a triangle ABC

Then, we know that the coordinates of centroid of the triangle are

R D Sharma Solutions For Class 10 Maths Chapter 14 Co-ordiniate Geometry ex 14.4 - 8

Given that the centroid for the triangle is (5/3, -1/3).

R D Sharma Solutions For Class 10 Maths Chapter 14 Co-ordiniate Geometry ex 14.4 - 9

⇒ x + 1 = 5 ⇒ y + 3 = -1

⇒ x = 4 ⇒ y = -4

Therefore, the coordinates of the third vertex C is (4, -4)

5. If (-2, 3), (4, -3) and (4, 5) are the mid-points of the sides of a triangle, find the coordinates of its centroid.

Solution:

R D Sharma Solutions For Class 10 Maths Chapter 14 Co-ordiniate Geometry ex 14.4 - 10

Let A (x1, y1), B (x2, y2) and C (x3, y3) be the vertices of triangle ABC.

Let D (-2, 3), E (4, -3) and F (4, 5) be the mid-points of sides BC, CA and AB respectively.

As D is the mid-point of BC

R D Sharma Solutions For Class 10 Maths Chapter 14 Co-ordiniate Geometry ex 14.4 - 11……. (1)

Similarly E and F are the mid-points of AC and AB

R D Sharma Solutions For Class 10 Maths Chapter 14 Co-ordiniate Geometry ex 14.4 - 12…….. (2)

And,

R D Sharma Solutions For Class 10 Maths Chapter 14 Co-ordiniate Geometry ex 14.4 - 13…… (3)

From (1), (2) and (3), we have

R D Sharma Solutions For Class 10 Maths Chapter 14 Co-ordiniate Geometry ex 14.4 - 14…….. (4)

Form (1) and (4), we get

R D Sharma Solutions For Class 10 Maths Chapter 14 Co-ordiniate Geometry ex 14.4 - 15

Thus, the coordinates of A are (10, -1)

From (2) and (4), we get

R D Sharma Solutions For Class 10 Maths Chapter 14 Co-ordiniate Geometry ex 14.4 - 16

Thus, the coordinates of B are (-2, 11)

From (3) and (4), we get

R D Sharma Solutions For Class 10 Maths Chapter 14 Co-ordiniate Geometry ex 14.4 - 17

Thus, the coordinates of C are (-2, -5)

Hence, the vertices of triangle ABC are A (10, -1), B (-2, 11) and C (-2, -5).

Therefore, the coordinates of the centroid of triangle ABC are

R D Sharma Solutions For Class 10 Maths Chapter 14 Co-ordiniate Geometry ex 14.4 - 18


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