Class 9 Maths Chapter 1 End of Exercises Question 13 is an important question for the Class 9 Maths CBSE Exam. This question is based on the concepts of midpoints and coordinates and requires the use of the midpoint formula to find the coordinates of the vertices of a triangle.
In this post, we have provided a step-by-step solution of Class 9 Maths Chapter 1 End of Exercises Question 13, along with a complete verification of the answer. Students can follow each step carefully and understand how the coordinates of A, B and C are calculated.
If you are preparing Class 9 Maths Chapter 1 End of Exercises Question 13, you can also watch the video solution given below for a clear explanation of the complete method.
13. The midpoints of the sides of triangle ABC are the points D, E, and F. Given that the coordinates of D, E, and F are (5, 1), (6, 5), and (0, 3), respectively, find the coordinates of A, B and C.
Solution
In this question, the coordinates of the midpoints of the three sides of triangle ABC are given. We have to use the midpoint formula to find the coordinates of the vertices A, B and C.
E is the mid point of BC and Coordinates of E are (6,5)
F is the mid point of AC and Coordinates of F are (0,3)
First taking all the equations of x coordinates and y coordinates
Taking the two pair of equations having x coordinates and solve them,putting value in third equation we get the value of all three x coordinates.
Similarly Taking the two pair of equations having y coordinates and solve them,putting value in third equation we get the value of all three y coordinates.
Watch the video
Watch the full Solution of Class 9 Maths Ganita Manjari chapter 1 Orienting Yourself: Uses of Coordinates
Click the link–Class 9 Maths Chapter 1 Orienting Yourself: Uses of Coordinates
FAQs About Class 9 Maths Chapter 1 End of Exercises Question 13
1. What is Class 9 Maths Chapter 1 End of Exercises Question 13?
Class 9 Maths Chapter 1 End of Exercises Question 13 asks students to find the coordinates of the vertices A, B and C of a triangle when the coordinates of the midpoints D, E and F of its three sides are given.
2. What is the answer to Class 9 Maths Chapter 1 End of Exercises Question 13?
The coordinates of the vertices A,B and C are: A(-1,-1),B(11,3) and C(1,7)
3. Which formula is used in this question?
The midpoint formula is used:
This formula helps us determine the midpoint of a line segment when the coordinates of its endpoints are known.If the coordinates of two points on the Cartesian plane are (x1 ,y1) and (x2 ,y2),then the coordinates of the midpoint (M) between them can be expressed using the following formula:
M = ((x₁ + x₂)/2, (y₁ + y₂)/2)
5. What are the coordinates of A in this question?
The coordinates of A are: (-1,-1)
6. What are the coordinates of B in this question?
The coordinates of B are: (11,3)
7.What are the coordinates of C in this question?
The coordinates of C are: (1,7)
8. How can the answer be verified?
The answer can be verified by calculating the midpoints of BC, CA and AB using the midpoint formula. The calculated midpoints should be: D=(5,1),E=(6,5),F=(0,3) which are exactly the points given in the question.
9. Is Class 9 Maths Chapter 1 End of Exercises Question 13 important for exams?
Yes. Class 9 Maths Chapter 1 End of Exercises Question 13 is a useful question for understanding the application of the midpoint formula and coordinates. Students should practise similar questions for better preparation for their CBSE Class 9 Maths examination.
10. Can I watch the video solution of this question?
Yes. You can watch the complete step-by-step video solution on this page. It explains how to use the midpoint coordinates to find the coordinates of all three vertices of triangle ABC.
Video Solution is here
CBSE Class 10 Maths NCERT Solutions
Continue your Class 10 Maths preparation with these useful resources from Future Study Point:
Class 10 Maths Chapter 1 – Real Numbers: Complete NCERT Exercise-Wise Video Solutions
Class 10 Maths Chapter 2 – Polynomials: Complete NCERT Solutions for Polynomials
Class 10 Maths Chapter 3 – Pair of Linear Equations in Two Variables: Complete NCERT Solutions
Class 10 Maths Chapter 4 Quadratic Equations: – Quadratic Equations complete NCERT video solutions
Class 10 Maths Chapter 5 Arithmetic Progression: Arithmetic Progression: complete video solution
Class 10 Maths Basic Sample Paper Solution: Practise with the Complete CBSE Basic Sample Paper Solution
Class 10 Maths Chapter 3 Most Important Questions Videos–Pair of Linear Equations in Two Variables
