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 1. नीचे दिए गए विकल्पों में से चुनें कि किस चतुर्थांश में एक बिंदु का भुज धनात्मक है।
A. I और II चतुर्थांश
B. मैं केवल चतुर्थांश
C. केवल द्वितीय चतुर्थांश
D. I और IV चतुर्थांश
उत्तर. (D) I और IV चतुर्थांश
प्रश्न 2. कार्तीय तल में एक बिंदु की स्थिति निर्धारित करने वाली क्षैतिज रेखा का क्या नाम है?
A. मूल
B. X- अक्ष
C. शाफ़्ट
D. चतुर्भाग
उत्तर. (B) एक्स-अक्ष
प्रश्न 3 निर्धारित करें कि दिए गए बिंदु (-5,2) और (2,-5) किस चतुर्थांश में स्थित होंगे:
A. क्रमशः II और III चतुर्थांश
B. क्रमशः I और IV चतुर्थांश
C. क्रमशः II और IV चतुर्थांश
D. एक ही चतुर्थांश में
उत्तर. (C) क्रमशः द्वितीय और चतुर्थ चतुर्थांश।
प्रश्न 4. दिए गए समीकरण से (x,y) निर्देशांक का मान निर्धारित करें: (x+2, 4) = (5, y-2)।
A. (3,6)
B. (2,1)
C. (7,12)
D. (6,3)
उत्तर. (A) (3,6)
प्रश्न 5. बिंदु (9,8) के y-अक्ष में दर्पण छवि के निर्देशांक होंगे
A. (-8,-9)
B. (-9,8)
C. (9,8)
D. (-9,-8)
उत्तर. (D) (-9,-8)
प्रश्न 6. y-अक्ष पर y-अक्ष की ऋणात्मक दिशा में 4 इकाई की दूरी पर स्थित एक बिंदु के निर्देशांक ज्ञात कीजिए?
A. (-4,0)
B. (4,0)
C. (5,4)
D. (0,-4)
उत्तर. (D) (0,-4)
प्रश्न 7. a का मान क्या होगा? x-अक्ष पर बिंदु P, Q, R को क्रमशः (2,0), (-6,0), और (3,a-3) के रूप में दिया गया है।
A. 0
B. 3
C. 2
D. -6
उत्तर. (B) 3
प्रश्न 8. दिए गए विकल्पों में से कौन सा बिंदु x-अक्ष के ऋणात्मक पक्ष पर स्थित है?
A. (-4,0)
B. (0,-4)
C. (3,2)
D. (5,7)
उत्तर. (A) (-4,0)
प्रश्न 9. नीचे दिए गए चित्र से, बिंदु Q के निर्देशांक क्या होंगे?
A. (3,-3.5)
B. (-3,-3.5)
C. (-3,3.5)
D. (3.5,3)
उत्तर. (B) (-3,-3.5)
प्रश्न 10. एक बिंदु M चतुर्थ चतुर्थांश में स्थित है। बिंदु M का निर्देशांक क्या होगा?
A. (A,B)
B. (-A,-B)
C. (-A,B)
D. (A,-B)
उत्तर. (D) (A,-B)
Question 1. Choose from the options given below in which quadrant the abscissa of a point is positive.
A. I and II Quadrants
B. I only quadrant
C. Second quadrant only
D. I and IV quadrants
Answer. (d) I and IV quadrants
Question 2. What is the name of the horizontal line that determines the position of a point in the Cartesian plane?
A.original
B.X-axis
C. shaft
D. Quadrant
Answer. (b) x-axis
Question 3 Determine in which quadrant the given points (-5,2) and (2,-5) will lie:
A. II and III quadrants respectively
B. I and IV quadrants respectively
C. II and IV quadrants respectively
D. In the same quadrant
Answer. (c) Second and fourth quartiles respectively.
Question 4. Determine the value of (x,y) coordinate from the given equation: (x+2, 4) = (5, y-2).
A.(3,6)
B.(2,1)
C.(7,12)
D.(6,3)
Answer. (A) (3,6)
Question 5. The coordinates of the mirror image in the y-axis of the point (9,8) will be
A.(-8,-9)
B.(-9,8)
C.(9,8)
D.(-9,-8)
Answer. (d) (-9,-8)
Question 6. Find the coordinates of a point located on the y-axis at a distance of 4 units in the negative direction of the y-axis?
A.(-4,0)
B.(4,0)
C.(5,4)
D.(0,-4)
Answer. (d) (0,-4)
Question 7. What will be the value of a? Points P, Q, R on x-axis are given as (2,0), (-6,0), and (3,a-3) respectively.
A. 0
B.3
C.2
D.-6
Answer. (B) 3
Question 8. Which point from the given options lies on the negative side of the x-axis?
A.(-4,0)
B.(0,-4)
C.(3,2)
D.(5,7)
Answer. (A) (-4,0)
Question 9. From the figure given below, what will be the coordinates of point Q?
A.(3,-3.5)
B.(-3,-3.5)
C.(-3,3.5)
D.(3.5,3)
Answer. (B) (-3,-3.5)
Question 10. A point M lies in the fourth quadrant. What will be the coordinate of point M?
A.(A,B)
B. (-A,-B)
C. (-A,B)
D. (A,-B)
Answer. (d) (a,-b)
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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