Find the best tutors and institutes for Class 10 Tuition
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)
Solution :
Given: The coordinates of the four points are $A(4, 5)$, $B(7, 6)$, $C(4, 3)$, and $D(1, 2)$.
To Find: The type of quadrilateral formed by these points, if any, and the reasons for the classification.
Step 1: Formula Definition
To determine the nature of the quadrilateral, we use the Distance Formula to find the lengths of the four sides ($AB, BC, CD, DA$) and the two diagonals ($AC, BD$).
The Distance Formula between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by:
$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$
Step 2: Calculating Side Lengths
- Length of AB: $\sqrt{(7 - 4)^2 + (6 - 5)^2} = \sqrt{3^2 + 1^2} = \sqrt{9 + 1} = \sqrt{10}$ units.
- Length of BC: $\sqrt{(4 - 7)^2 + (3 - 6)^2} = \sqrt{(-3)^2 + (-3)^2} = \sqrt{9 + 9} = \sqrt{18} = 3\sqrt{2}$ units.
- Length of CD: $\sqrt{(1 - 4)^2 + (2 - 3)^2} = \sqrt{(-3)^2 + (-1)^2} = \sqrt{9 + 1} = \sqrt{10}$ units.
- Length of DA: $\sqrt{(4 - 1)^2 + (5 - 2)^2} = \sqrt{3^2 + 3^2} = \sqrt{9 + 9} = \sqrt{18} = 3\sqrt{2}$ units.
Step 3: Calculating Diagonal Lengths
- Length of AC: $\sqrt{(4 - 4)^2 + (3 - 5)^2} = \sqrt{0^2 + (-2)^2} = \sqrt{4} = 2$ units.
- Length of BD: $\sqrt{(1 - 7)^2 + (2 - 6)^2} = \sqrt{(-6)^2 + (-4)^2} = \sqrt{36 + 16} = \sqrt{52} = 2\sqrt{13}$ units.
Step 4: Analysis and Conclusion
From the calculations:
1. Opposite sides are equal: $AB = CD = \sqrt{10}$ and $BC = DA = 3\sqrt{2}$.
2. Diagonals are unequal: $AC = 2$ and $BD = \sqrt{52}$.
Since the opposite sides are equal and the diagonals are not equal, the quadrilateral satisfies the properties of a parallelogram.
Final Answer: The points form a parallelogram.
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.
- Q4: Check whether (5, – 2), (6, 4) and (7, – 2) are the vertices of an isosceles triangle.
- 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)
- 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
Hi, I'm Ravi Shankar, a Mathematics educator with 10+ years of teaching experience. I help Class 10 students strengthen their concepts, improve application skills, and prepare systematically for important examinations. At this stage, simply knowing formulas isn't enough. Students need to recognise the appropriate method, interpret questions correctly, solve efficiently and avoid losing marks through preventable mistakes. My classes focus on: • Concept mastery • Algebra and functions • Geometry • Trigonometry • Statistics and probability • Application-based problems • Multi-step questions • Past-paper practice • Error analysis • Time management and exam strategy I use regular assessments to identify recurring mistakes and areas requiring additional attention. My approach: Concept → Application → Problem Solving → Exam Practice → Analysis The goal is to help students approach examinations with greater confidence, accuracy, and consistency. Book an introductory session to understand where your child currently stands and what needs to improve.
I highly appreciate Sir’s dedication and clarity in teaching. His systematic approach helped me score confidently in board examinations.
Ability to connect with children (or with older students), on a personal level. communication and social skills.Teaching can be quite satisfying for people who do it well. I know this because I am a teacher, too. Although I do not think I'm always the best teacher, do I know that the majority of my students love me, and I guess this is partly why good things happen in my classroom. I have spent a lot of time thinking about and done a lot of research in to the question of what characteristics make a teacher effective and how I can succeed in the classroom. Although every great teacher has their own special, unique style, I have found that there are nine specific universal qualities that are necessary for anyone who wants to teach effectively, whether they want to teach in an elementary school or a university. If any teacher possesses the following characteristics and qualities, he/she can become a very good teacher with large fan base.
Have taught in school for 10th grade students.
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.
Good class. Sir explained concepts well, i understood the concepts easily, and sir also cleared all my doubts.
I am an experienced tutor with 4 years of experience in this field. I completed my BE in the year 2014. I have tutored students for Spoken English, BTech Tuition, C Language, C++ Language, CAD, CE and COMEDK Coaching. I can conduct classes at Student's Home, My place and Online via a different medium to students from International, CBSE, State, ICSE/ISC Board. I follow different techniques while teaching so, that my students are engaged positively. To make learning fun and easier, I use creative and innovative ideas.
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
Download free CBSE - Class 10 Mathematics Coordinate geometry EXERCISE 7.1 worksheets
Download Now