Welcome to JNVMaths.com, your trusted companion on the path to success in the Jawahar Navodaya Vidyalaya Class 9 Entrance Exam. In this extensive guide, we'll dive deep into the realm of Coordinate Geometry, offering you a comprehensive understanding of this vital topic that will help you excel in your upcoming exam.
Chapter 1: Understanding Coordinate Geometry Coordinate Geometry is a pivotal branch of mathematics that combines algebraic and geometric concepts. In this chapter, we will explore the fundamental elements that underpin Coordinate Geometry and set the stage for more complex topics.
1.1. Introduction to the Cartesian Plane: We'll begin by introducing you to the Cartesian Plane, the foundation of Coordinate Geometry. Learn how to plot points and understand the axes.
1.2. Coordinates and Quadrants: Delve into the concept of coordinates and quadrants, as well as how to identify points in different quadrants.
1.3. Distance Formula: Master the distance formula to calculate the distance between two points on the coordinate plane. 1.4. Section Formula: Understand how to find the coordinates of a point dividing a line segment into a given ratio.
Chapter 2: Equations of Lines In this chapter, we'll take a closer look at the equations of lines and how they are represented in Coordinate Geometry.
2.1. Slope of a Line: Learn how to calculate the slope of a line and understand its significance in determining the inclination of a line.
2.2. Equation of a Line: Explore different forms of equations of lines, including point-slope form, slope-intercept form, and general form.
2.3. Parallel and Perpendicular Lines: Understand the relationship between the slopes of parallel and perpendicular lines. Chapter 3: Geometry and Co-ordinate Geometry Coordinate Geometry isn't just about plotting points and drawing lines; it also has practical applications in geometric problem-solving.
3.1. Midpoint Formula: Discover how to find the midpoint of a line segment and its role in geometry.
3.2. Area of a Triangle: Learn how to calculate the area of a triangle using Coordinate Geometry.
3.3. Collinearity and Concurrency: Explore how Coordinate Geometry helps determine if points are collinear or lines are concurrent. Chapter 4: Advanced Concepts and Problem Solving In the final chapter, we'll tackle more complex concepts and demonstrate how to solve challenging problems using Coordinate Geometry.
4.1. Locus and its Equations: Understand what a locus is and how to derive equations representing loci.
4.2. Coordinate Geometry in Real Life: Explore real-life applications of Coordinate Geometry, from navigation to architecture.
4.3. Coordinate Geometry in Coordinate Systems: Learn how Coordinate Geometry extends beyond the Cartesian Plane into other coordinate systems.
प्रश्न 11. निर्धारित करें कि बिंदु (-3,-5) किस चतुर्थांश में स्थित होगा।
A. मैं चतुर्थांश
B. द्वितीय चतुर्थांश
C. तृतीय चतुर्थांश
D. चतुर्थ चतुर्थांश
उत्तर. तृतीय चतुर्थांश
प्रश्न 12. y-अक्ष पर सभी बिंदुओं का भुज क्या होगा?
A. 1
B. 0
C. -1
D. कोई संख्या
उत्तर. (B) 0
प्रश्न 14. कार्तीय तल में बिंदु का स्थान निर्धारित करने वाली क्षैतिज और ऊर्ध्वाधर रेखाओं के प्रतिच्छेदन से बनने वाले खंडों के नाम बताइए:
A. मूल
B. X- अक्ष
C. शाफ़्ट
D. चतुर्भाग
उत्तर. (D) चतुर्भुज
प्रश्न 15. बिंदु Q(1,2), R(-2,-3), और S(2,-3) किस चतुर्थांश में स्थित होंगे?
A. मैं चतुर्थांश
B. चतुर्थ चतुर्थांश
C. तृतीय चतुर्थांश
D. एक ही चतुर्थांश में मत रहो
उत्तर. (D) एक ही चतुर्थांश में न रहें
प्रश्न 16. यदि किसी बिंदु का x निर्देशांक 0 है तो यह निर्धारित किया जाता है कि बिंदु किस चतुर्थांश में स्थित होगा:
A. मैं चतुर्थांश
B.द्वितीय चतुर्थांश
C. X- अक्ष
D. Y-अक्ष
उत्तर. (D) Y-अक्ष
प्रश्न 17. x-अक्ष पर सभी बिंदुओं की कोटि है
A. -1
B. 1
C. 0
D. कोई संख्या
उत्तर. (C) 0
प्रश्न 18. x-अक्ष पर सभी बिंदुओं के लिए, भुज (abscissa) है:
A. 0
B. 1
C. 2
D. कोई संख्या
उत्तर. (D) कोई भी संख्या
प्रश्न 19. यदि किसी बिंदु P की x-अक्ष से लंब दूरी 7 इकाई है और लंब का पाद x-अक्ष की ऋणात्मक दिशा पर है, तो बिंदु p का मान क्या होगा?
A. Y-निर्देशांक = 7 या -7 ही
B. Y- निर्देशांक = केवल 7
C. Y-निर्देशांक = -7 केवल
D. एक्स-निर्देशांक = -7
उत्तर. (A) वाई-निर्देशांक = 7 या -7 ही
प्रश्न 20. दो बिंदुओं P और Q के निर्देशांक क्रमशः (-7,5) और (-6,9) दिए गए हैं। (P का भुज) – (Q का भुज) का मान क्या होगा?
A. -3
B. 1
C. -2
D. -1
उत्तर. (D)-1
Question 11. Determine in which quadrant the point (-3,-5) will lie.
A. First Quadrant
B. Second Quadrant
C. Third Quadrant
D. Fourth Quadrant
Answer. Third Quadrant
Question 12. What will be the abscissa of all the points on y-axis?
A.1
B.0
C.-1
D. Any number
Answer. (b) 0
Question 14. Name the segments formed by the intersection of horizontal and vertical lines determining the location of a point in the Cartesian plane:
A.original
B.X-axis
C. shaft
D. Quadrant
Answer. (d) quadrilateral
Question 15. In which quadrant will the points Q(1,2), R(-2,-3), and S(2,-3) lie?
A. I Quadrant
B. Fourth Quadrant
C. Third Quadrant
D. Do not stay in the same quadrant
Answer. (d) not stay in the same quadrant
Question 16. If the x coordinate of a point is 0 then it is determined in which quadrant the point will lie:
A. I Quadrant
B.Second Quadrant
C.X-axis
D. shaft
Answer. (d) Y-axis
Question 17. The ordinate of all the points on the x-axis is
A.-1
B.1
C. 0
D. Any number
Answer. (c) 0
Question 18. For all points on the x-axis, the abscissa is:
A. 0
B.1
C.2
D. Any number
Answer. (d) any number
Question 19. If the perpendicular distance of a point P from the x-axis is 7 units and the foot of the perpendicular is on the negative direction of the x-axis, then what will be the value of the point p?
A. Y-coordinate = 7 or -7 only
B. Y-coordinate = 7 only
C. Y-coordinate = -7 only
D.
Answer. (a) Y-coordinate = 7 or -7 only
Question 20. The coordinates of two points P and Q are given as (-7,5) and (-6,9) respectively. What will be the value of (abscissa of P) – (abscissa of Q)?
A.-3
B.1
C.-2
D.-1
Answer. (d)-1
Conclusion: By the end of this comprehensive guide, you'll be well-versed in Coordinate Geometry, ready to tackle any question that comes your way in the JNV Class 9 Entrance Exam. Stay tuned for more helpful content and exam tips on JNVMaths.com as you continue your journey toward success. Good luck!
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