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NCERT New Syllabus Mathematics
Class: 10
Exercise 7.1
Topic: Coordinate Geometry
Understanding Coordinate Geometry: A Key Concept in Class 10 Mathematics
Coordinate Geometry, often called Cartesian Geometry, bridges the gap between algebra and geometry, allowing us to visualize geometric shapes and solve problems using algebraic equations. It’s a fascinating tool for plotting points, lines, and curves on a plane, all through coordinates. In Class 10, you’ll explore concepts like the distance between two points, the section formula, and the area of a triangle, all of which are essential building blocks for higher-level mathematics and real-life applications.
This chapter enhances your spatial reasoning and gives you the foundation to tackle more complex problems in trigonometry, calculus, and beyond. Let's dive into the core concepts and see how algebra and geometry come together to solve some exciting problems!
EXERCISE 7.1
Q 1. Find the distance between the following pairs of points :
(i) (2, 3), (4, 1) (ii) (– 5, 7), (– 1, 3) (iii) (a, b), (– a, – b)
Solution:
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 discussed in Section 7.2.
Solution:
Q 3. Determine if the points (1, 5), (2, 3) and (– 2, – 11) are collinear.
Solution:
Q 4. Check whether (5, – 2), (6, 4), and (7, – 2) are the vertices of an isosceles
triangle.
Solution:
Q 5. In a classroom, 4 friends are seated at points A, B, C, and D as shown
in following figure. 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 the distance formula, find which of them is correct.
Solution:
1) First we will find the coordinates of points A, B, C, and D, See the following
figure.
Q 6. 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)
(ii) (–3, 5), (3, 1), (0, 3), (–1, – 4)
(iii) (4, 5), (7, 6), (4, 3), (1, 2)
Solution:
(i) (– 1, – 2), (1, 0), (– 1, 2), (– 3, 0)
(ii) (–3, 5), (3, 1), (0, 3), (–1, – 4)
5) Therefore the points A, B, C, and D will not form a quadrilateral.
Q 7. Find the point on the x-axis which is equidistant from (2, –5)
and (– 2, 9).
Solution:
Q 8. Find the values of y for which the distance between the points
P(2, – 3) and Q(10, y) is 10 units.
Solution:
Q 9. 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.
Solution:
from the point (3, 6) and (– 3, 4).
Solution:
Conclusion
Coordinate Geometry offers a powerful way to link algebra with geometric concepts, providing a deeper understanding of spatial relationships. The techniques covered in this chapter, such as finding distances, midpoints, and areas, lay a solid foundation for more advanced topics in mathematics. By mastering these concepts, students enhance their problem-solving skills and develop a critical toolset that will be invaluable in fields like engineering, physics, and computer science.
Continue practicing these methods, and you’ll find that coordinate geometry is useful and an exciting area of math that transforms abstract numbers into meaningful visual solutions.
Keep learning, keep exploring!
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