Find the best tutors and institutes for Class 10 Tuition
Q4:
Check whether (5, – 2), (6, 4) and (7, – 2) are the vertices of an isosceles triangle.
Solution :
Given: Three points in a Cartesian plane: $A(5, -2)$, $B(6, 4)$, and $C(7, -2)$.
To Find: Determine whether the triangle formed by these vertices is an isosceles triangle.
Definition: An isosceles triangle is a triangle in which at least two sides are equal in length.
Formula: The distance $d$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the Distance Formula:
$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$
Step 1: Calculate the length of side $AB$
Let $A = (5, -2)$ and $B = (6, 4)$.
$AB = \sqrt{(6 - 5)^2 + (4 - (-2))^2}$
$AB = \sqrt{(1)^2 + (4 + 2)^2}$
$AB = \sqrt{1^2 + 6^2}$
$AB = \sqrt{1 + 36}$
$AB = \sqrt{37}$ units
Step 2: Calculate the length of side $BC$
Let $B = (6, 4)$ and $C = (7, -2)$.
$BC = \sqrt{(7 - 6)^2 + (-2 - 4)^2}$
$BC = \sqrt{(1)^2 + (-6)^2}$
$BC = \sqrt{1 + 36}$
$BC = \sqrt{37}$ units
Step 3: Calculate the length of side $AC$
Let $A = (5, -2)$ and $C = (7, -2)$.
$AC = \sqrt{(7 - 5)^2 + (-2 - (-2))^2}$
$AC = \sqrt{(2)^2 + (-2 + 2)^2}$
$AC = \sqrt{2^2 + 0^2}$
$AC = \sqrt{4}$
$AC = 2$ units
Step 4: Comparison and Conclusion
We have found the lengths of the sides to be:
$AB = \sqrt{37}$
$BC = \sqrt{37}$
$AC = 2$
[Since $AB = BC = \sqrt{37}$, two sides of the triangle are equal in length.]
Final Answer: Yes, the points (5, – 2), (6, 4) and (7, – 2) are the vertices of an isosceles triangle because two of its sides are equal in length.
More Questions from Class 10 Mathematics Coordinate geometry EXERCISE 7.1
- Q1(i): Find the distance between the following pairs of points : (i) (2, 3), (4, 1)
- Q1(ii): Find the distance between the following pairs of points : (ii) (– 5, 7), (– 1, 3)
- Q1(iii): Find the distance between the following pairs of points : (iii) ($a$, $b$), (– $a$, – $b$)
- Q10: Find a relation between $x$ and $y$ such that the point ($x$, $y$) is equidistant from the point (3, 6) and (– 3, 4).
- Q2: Find the distance between the points (0, 0) and (36, 15). Can you now find the distance between the two towns A and B.
- Q3: Determine if the points (1, 5), (2, 3) and (– 2, – 11) are collinear.
- Q5: 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.
- Q6(i): 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)
- Q6(ii): Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer: (ii) (–3, 5), (3, 1), (0, 3), (–1, – 4)
- Q6(iii): Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer: (iii) (4, 5), (7, 6), (4, 3), (1, 2)
- Q7: Find the point on the x-axis which is equidistant from (2, –5) and (–2, 9).
- Q8: Find the values of $y$ for which the distance between the points P(2, – 3) and Q(10, $y$) is 10 units.
- Q9: 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.
CBSE Solutions for Class 10 Mathematics Coordinate geometry
Chapters in CBSE - Class 10 Mathematics
Top Tutors who teach Coordinate geometry
Shankar Vihar, Delhi
18 yrs of
Exp
Student's Home
We are teaching 8th, 9th,10th,11th,12th for the last 12 years and providing 95%+ in our subjects. We are giving best results in DELHI CANTT and South Delhi region.
Top Tutor
Thindal, Erode
10 yrs of
Exp
3 students
49 hrs of classes completed
450
per hour
Online Classes
Student's Home
Hello,I am an experienced Maths tutor with over 10 years of teaching experience. I specialize in helping students from classes 10-12 improve their conceptual understanding and exam performance.Based on your requirements,I can create a personalized study plan and provide regular practice with doubt clearing sessions. I would be happy to discuss your goals and arange a demo class.
Attending these online tutoring sessions has been an amazing experience for me for my class 10 CBSE math syllabus. The tutor has been very patient in teaching me the concepts behind every formula. He does not encourage rote learning but makes the student understand the logic and reasoning behind every step using a whiteboard on his camera, making the student feel right in the classroom while eliminating all doubts. Though he excels in tutoring students of all classes and grades, my marks and confidence levels have improved consistently under his guidance, and I recommend him to clear any exam with flying colors.
Top Tutor
Kaloor, Kochi
12 yrs of
Exp
2 students
2 hrs of classes completed
500
per hour
Online Classes
Student's Home
Tutor's home
With 12 years of teaching experience, I specialize in concept-based instruction, catering to both weaker students and advanced learners. I help struggling students grasp core concepts while providing advanced-level teaching to high achievers, enabling them to consistently reach 95% or higher in their academic performance.
Top Tutor
Kazipet, Warangal
2 yrs of
Exp
1 student
50 hrs of classes completed
Online Classes
Student's Home
Tutor's home
I have 5years of teaching experience where I implement Inductive ,Deductive teaching techinques in mathematics. I begin the teaching concepts of maths with basic level to high level which ensures the teaching learning process occurs even a below average student I make special work sheets for the brain nutrient students and also to the below average students ,so that helps students to become learn individually according to their level. In teaching maths concepts regarding Geometry , Trignometry and Areas and Circles here I use the concrete to semi concrete from thier i take them to abstract so child can easily familiar to the concept, teaching learning process occurs in a positive way. In teaching maths I use heuristic method which creates an enthusiasm among the students to learn maths subject and it eradicate the fear of maths from the students. As a teacher I teach according to the students taste and their interests, so teaching learning process will be occurred in a meaningful way. I observe the individual difference of the students while teaching, so that I can plan to teach according individual difference of the different students in the classroom. I use remedial class for the slow learners to develop in the subject. In this remedial session I mostly concentrating on the basic of maths subject so children can overcome the previous misunderstanding concepts regarding maths and here it will be taught his doubts regarding subject will be clarified. By teaching maths subject I make students all round development which is very valuable in the life.
Super Tutor
Saheed Nagar, Bhubaneswar
11 yrs of
Exp
35 students
627 hrs of classes completed
499
per hour
Online Classes
▪️Class 10 Board Specialist ▪️IGCSE / IB / CBSE / ICSE / Focus ▪️Syllabus-Aligned Teaching ▪️Concept Clarity First ▪️Exam-Oriented Preparation ▪️Board Pattern Mastery ▪️Previous Year Questions Practice ▪️Structured Lesson Planning ▪️Step-by-Step Problem Solving ▪️Time Management Training ▪️Weekly Tests & Mock Exams ▪️Performance Tracking ▪️Targeted Weak Area Support ▪️Answer Writing Techniques ▪️Regular Parent Updates ▪️Result-Driven Approach
Find more Tutor for Coordinate geometry in your City
- Bangalore Mathematics Tutors
- Delhi Mathematics Tutors
- Chennai Mathematics Tutors
- Gurgaon Mathematics Tutors
- Noida Mathematics Tutors
- Hyderabad Mathematics Tutors
- Mumbai Mathematics Tutors
- Ghaziabad Mathematics Tutors
- Chandigarh Mathematics Tutors
- Pune Mathematics Tutors
- Jaipur Mathematics Tutors
- Surat Mathematics Tutors
