NCERT Exemplar Solutions for Class 10 Math Chapter 7 Coordinate Geometry for 2025-26 Board Exams:
NCERT Exemplar Class 10 Maths Chapter 7 Coordinate Geometry is available in PDF format for students to study for CBSE examinations. Experts created these sample questions and solutions in accordance with the CBSE Syllabus. The sample may also be used as a study aid, and it appears that it will assist students in improving their math fluency and tackling even the most challenging problems that may be posed in the CBSE first and second term exams.
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Students will be exposed to several formulations such as the distance and section formulas in Chapter 7 of NCERT Exemplar Class 10 Solutions, and they will be expected to learn how to apply them appropriately. Topics such as the area of a triangle is also covered in this chapter, and students are required to work on problems based on them. While this is the chapter's major goal, it also helps students focus on applying coordinate geometry ideas to real-world settings.
NCERT Exemplar Solutions for Class 10 Math Chapter 7 Coordinate Geometry | Free PDF Download
Topics Covered in this chapter:
- Calculating the distance between two places in two different coordinates
- Finding the coordinates of the point that splits a line segment using the section formula
- Using coordinate points to calculate the area of triangles
NCERT Exemplar Solutions Class 10 of All Chapters:
NCERT EXEMPLAR SOLUTIONS CLASS 10 CHAPTER 1 REAL NUMBERS
NCERT EXEMPLAR SOLUTIONS CLASS 10 CHAPTER 2 POLYNOMIALS
NCERT EXEMPLAR SOLUTIONS CLASS 10 CHAPTER 3 PAIR OF LINEAR EQUATIONS IN 2 VARIABLES
NCERT EXEMPLAR SOLUTIONS CLASS 10 CHAPTER 4 QUADRATIC EQUATIONS
NCERT EXEMPLAR SOLUTIONS CLASS 10 CHAPTER 5 ARITHMETIC PROGRESSIONS
NCERT EXEMPLAR SOLUTIONS CLASS 10 CHAPTER 6 TRIANGLES
NCERT EXEMPLAR SOLUTIONS CLASS 10 CHAPTER 7 COORDINATE GEOMETRY
NCERT EXEMPLAR SOLUTIONS CLASS 10 CHAPTER 8 INTRODUCTION TO TRIGONOMETRY & ITS EQUATION
NCERT EXEMPLAR SOLUTIONS CLASS 10 CHPATER 9 SOME APPLICATIONS OF TRIGONOMETRY
NCERT EXEMPLAR SOLUTIONS CLASS 10 CHAPTER 10 CIRCLES
NCERT EXEMPLAR SOLUTIONS CLASS 10 CHAPTER 11 CONSTRUCTIONS
NCERT EXEMPLAR SOLUTIONS CLASS 10 CHAPTER 12 AREAS RELATED TO CIRCLES
NCERT EXEMPLAR SOLUTIONS CLASS 10 CHAPTER 13 SURFACE AREAS AND VOLUMES
NCERT EXEMPLAR SOLUTIONS CLASS 10 CHAPTER 14 STATISTICS AND PROBABILITY
NCERT EXEMPLAR SOLUTIONS CLASS 10 CHAPTER 15 PROBABILITY
Distance Formula
Identifying the line segment's mid-point that connects the coordinate points. Determining the mid-point of the line segment that links the coordinate points.
The coordinating point on the x-axis are (x, 0) and the coordinating point on the y-axis are (0, y).
To find the distance between any two points P (x1, y1) and q (x2, y2)
Draw a PR and QS perpendicular to the x-axis
A Perpendicular is drawn from the point P on QS to meet it at the point T.
Then, OR = x1, OS = X2. So, RS = X2 = X1= PT SQ =y2, ST = PR = y1. So, QT = y2 - y1 Applying Pythagoras Triangle in A PTQ, we get
PQ2 = PT2 + QT2
PQ2 = [(x2 - x1)2]2 + [(y2 - y1)2]2
PQ = (x2 - x1) ² + (y2 - y1)2
Or PQ = (x1 - x2)2 + (y1- y2)2
The distance between the points P (x1, y1) and Q (x2, y2) is
PQ = (x2 - x1) 2 + (y2 - y1)2, which is called the distance formula.
Distance formula = (x2 - x1) 2 + (y2 - y1)2
Section Formula
The coordinates of a point that splits a line segment into a ratio of m:n is found using section formula class 10 to discover the coordinates of a point that split the Internally or externally, breaks a line segment into a m:n ratio. In coordinate geometry, the section formula is usually used to calculate the incenter, centroid, and excentres of a triangle. Other topics, such as Physics, employ the section formula.
The coordinates (x, y) of a point O that breaks the line segment connecting the points P (x1, y1) and Q (x2, y2) in the ratio m1: m2 are:
- Internal division section formula: O (x, y) = x = m1x2 + m2x1/m1+ m2 and y = my2+ m2y1/m1+ m2
- For external division, use the following formula:
x = ((m1x2 - m2x1)/m1+ m2, y = (m1y2 - m2y1)/m1+ m2)
O (x, y) O (x, y) O (x, y) O (x, y) O (x, y) O (x, y) O (x, y) O (x, y) O (x, y) O (x, y)
M (x, y) = [(x2 + x1)/ 2, (y2 + y1)/2] is the midpoint formula.
Example: Let S (x, y) be the purpose that divides the road phase.
The points P (5, - 5) and Q (10, 5) within the quantitative relation 4:1 internally.
Solution: Let S (x, y) be the point that divides the line segment.
Using the section formula, we get
x = 4(10) + 1(5) /4 +1= 9
y =4(5) +1(-5)/4 +1= 3
Therefore, (9, 3) is the required point.
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Frequently Asked Questions:
In NCERT, what does coordinate geometry mean?
Coordinate Geometry is viewed together of the foremost fascinating mathematical idea with pure mathematics analytic geometry (also called analytic geometry) could be a branch of arithmetic that discusses the link between geometry and pure mathematics victimization graphs comprising curves and contours.
Geometric options are enclosed in pure mathematics, permitting students to resolve geometric issues. It is a kind of pure mathematics within which the coordinates of points on a plane are expressed as associate ordered combine of integers. This chapter is additionally thought to be one in all the foremost crucial in terms of examination preparation.
Is it tough to learn Chapter 7 of NCERT Solutions for Class 10 Math?
No, NCERT good example Solutions for sophistication ten Maths Chapter seven isn't robust to understand. It's one in all lot of pars taking topics in school ten, and it will be continued in additional education moreover. Students are going to be able to answer the elemental sums of integration a lot of effectively if they need a decent understanding of integral formulae. deciding the gap between 2 points, cacophonic lines within the m:n quantitative relation, finding the center of a line, computing the world of a triangle within the sheet, and alternative tasks want a radical understanding of analytical geometry.
Conclusion
Students may download the NCERT Exemplar for Chapter 7 – Coordinate Geometry in Free PDF format for free to improve their comprehension of all topics and practice questions more efficiently. To solve exemplars for all of Maths Class 10's chapters. Class 10 students should solve sample papers and previous year question papers to have a sense of the kind of problems that will be asked in the Coordinate Geometry chapter. They may also use online study products, which include notes, example books, Maths NCERT Solutions for Class 10, and question papers, to prepare for the test.
