Cbse Class 10 Mathematics Chapter 7 Important Questions - Coordinate Geometry

Strengthen your preparation for the CBSE Class 10 Board Exams with this guide on CBSE Class 10 Mathematics Chapter 7 Important Questions - Coordinate Geometry. Explore key concepts like physical and chemical properties, reactivity series, and practical applications to excel in exams confidently.

Cbse Class 10 Mathematics Chapter 7 Important Questions - Coordinate Geometry

Here are 50 important questions on Cbse Class 10 Mathematics Chapter 7 Important Questions - Coordinate Geometry

1. What is the distance formula used to find the distance between two points in a coordinate plane?
2. Calculate the distance between the points (3, 4) and (7, 1).
3. How do you determine if three points are collinear using their coordinates?
4. Given points A(1, 2), B(4, y), and C(3, 5), find the value of y for which these points are collinear.
5. What is the section formula used for finding a point dividing a line segment in a given ratio?
6. Find the coordinates of the point that divides the line segment joining (2, 3) and (8, 7) in the ratio 3:5.
7. Define the concept of midpoint in coordinate geometry.
8. Calculate the midpoint of the line segment joining points (6, -2) and (-4, 8).
9. How can you find the area of a triangle formed by three points in a coordinate plane?
10. Calculate the area of a triangle with vertices at (0, 0), (4, 0), and (0, 3).
11. Explain how to determine if a quadrilateral is a parallelogram using its vertices.
12. Given points A(1, 2), B(4, y), C(x, 6), and D(3, 5), find x and y if ABCD is a parallelogram.
13. What is the formula to find the slope of a line given two points?
14. Calculate the slope of the line passing through points (2, 3) and (4, 7).
15. Explain how to find the equation of a line given its slope and a point on it.
16. Write the equation of a line with slope m = −2 that passes through point (1, 4).
17. How do you determine whether two lines are parallel using their slopes?
18. If two lines have slopes m1 = 3 and m2 = −1/3, are they parallel or perpendicular?
19. Define what it means for two lines to be perpendicular in terms of their slopes.
20. Find the coordinates of a point that is equidistant from (2, -5) and (-2, 9).
21. Explain how to use distance formulas to find if a point lies on a given line.
22. How can you verify if four points form a rectangle?
23. Given points A(-1, -1), B(1, -1), C(1, 1), and D(-1, 1), determine if they form a square.
24. What is the relationship between coordinates of points that lie on the same line?
25. Find the coordinates of point P that divides segment AB in ratio 3 : 2 where A(2, 3) and B(8, 9).
26. How do you find an equation of a circle given its center and radius?
27. Write down the standard form equation of a circle centered at (h, k) with radius r.
28. If the center of a circle is at (3, -2) and its radius is 5, what is its equation?
29. Describe how to find distances between multiple points in one calculation.
30. Calculate distances between points A(0,0), B(3,-4), and C(-5,-5).
31. Explain how to derive an equation for a line given two points.
32. Given points A(-2, -2) and B(2, -4), find coordinates of point P such that AP = 7/3 AB.
33. What method would you use to find coordinates that trisect a segment joining two points?
34. Find coordinates of points that trisect segment joining A(-1, -1) and B(5, 5).
35. Explain how to use determinants to find areas of triangles formed by three points.
36. Calculate area using determinants for triangle formed by A(0,0), B(4,0), C(0,3).
37. How can you prove that two triangles are congruent using coordinate geometry?
38. Given triangle vertices A(0,0), B(a,b), C(c,d), write conditions for congruence.
39. Determine if points A(1,-1), B(-1,-1), C(-1,-3) form an isosceles triangle.
40. How do you calculate lengths of sides in any triangle using coordinate geometry?
41. Find lengths of sides for triangle with vertices at (0,0), (4,-3), (-3,-4).
42. Explain how to derive equations for parallel lines through specific coordinates.
43. Write an equation for line parallel to y = 2x + 3 passing through point (1,-2).
44. Discuss methods for finding intersections between two lines given their equations.
45. Find intersection point for lines y = x + 2 and y = -x + 4.
46. Describe how to locate centroids in triangles using their vertex coordinates.
47. Find centroid for triangle with vertices at (0,0), (6,0), (3,9).
48. What steps would you take to graphically represent coordinate geometry problems?
49. Discuss applications of coordinate geometry in real-world scenarios like navigation or architecture.
50. How can transformations such as translation or rotation be represented in coordinate geometry?

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These questions cover various aspects of Coordinate Geometry, including their properties, reactions, uses, and applications as presented in the document provided, ensuring comprehensive coverage of key topics within this chapter on Coordinate Geometry.

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Class 10 Coordinate Geometry Notes

The chapter “Coordinate Geometry” in Class 10 Science explores the fundamental properties, reactivity, and applications of Coordinate Geometry. Below is a detailed explanation of the key topics covered in this chapter based on class 10 maths syllabus:

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1. Introduction to Coordinate Geometry:

Coordinate Geometry is the study of geometry using a coordinate system. It involves the representation of geometric figures in a coordinate plane using a set of coordinates. In two-dimensional geometry, the coordinates are expressed as pairs of numbers (x,y), where:

• x is the abscissa (distance from the y-axis).
• y is the ordinate (distance from the x-axis).

The Cartesian coordinate system consists of two perpendicular axes:

• The x-axis (horizontal).
• The y-axis (vertical).

The intersection of these axes is called the origin (0, 0). Points on the plane are described by coordinates (x,y).

2. Graphs of Linear Equations:

A linear equation in two variables has the general form:

ax + by + c = 0

Where:

• a, b, and c are constants.
• x and y are the variables.

The graph of a linear equation is a straight line. Some special cases are:

• If y = mx + c, this is the slope-intercept form of a straight line, where:some text
  • mmm is the slope of the line.
  • ccc is the y-intercept (the point where the line crosses the y-axis).

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Conclusion:

In Metals and Non-Metals, students learn to distinguish between the physical and chemical properties of metals and non-metals, along with their reactivity series.

Mastering these concepts is essential for tackling questions in the CBSE Class 10 Board Exams.

Focusing on CBSE Class 10 Science Chapter 3 Important Questions - Metals and Non-Metals and reviewing related sample papers will enhance understanding and exam performance. Consistent revision and well-organized notes are key to acing this chapter.

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Other Chapters:

Chapter 1 Chemical Reactions And Equations

Chapter 2 Acids, Bases, And Salts

Chapter 3 Metals And Non-Metals

Chapter 4 Carbon and its compounds

Chapter 5 Life Processes

Chapter 6 Control And Coordination

Chapter 7 How Do Organisms Reproduce?

Chapter 8 Heredity And Evolution

Chapter 9 Light – Reflection And Refraction

Chapter 10 The Human Eye And The Colourful World

Chapter 11 Electricity

Chapter 12 Magnetic Effects Of Electric Current

Chapter 13 Our Environment

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Also Refer:

Class 10 Science NCERT Book PDF

Class 10 Science Sample Papers