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Chapter Analysis
Beginner11 pages • EnglishQuick Summary
This chapter on Coordinate Geometry introduces the concepts of locating a point in a plane using Cartesian coordinates. It explains the use of the x-axis and y-axis to create a coordinate plane, defining the origin where these axes intersect. The chapter elaborates on quadrants and the convention of representing point coordinates as (x, y). It also touches upon the historical development by René Descartes and emphasizes understanding and practicing the placement of points in different quadrants.
Key Topics
- •Cartesian Plane
- •Coordinate Axes
- •Quadrants
- •Coordinates and their Representation
- •Origin
- •Reflection in Coordinate Geometry
- •Distances from Axes
Learning Objectives
- ✓Understand the concept of a coordinate plane and its uses.
- ✓Learn to identify quadrants based on point coordinates.
- ✓Gain proficiency in plotting points based on given coordinates.
- ✓Distinguish between x-coordinate (abscissa) and y-coordinate (ordinate).
- ✓Apply knowledge of Cartesian coordinates to solve geometry problems.
- ✓Appreciate the historical development of coordinate geometry.
Questions in Chapter
What is the name of horizontal and the vertical lines drawn to determine the position of any point in the Cartesian plane?
Answer: The horizontal line is called the x-axis, and the vertical line is called the y-axis.
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What is the name of each part of the plane formed by these two lines?
Answer: Each part is called a quadrant.
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Write the name of the point where these two lines intersect.
Answer: The point is called the origin.
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See Fig.3.14, and write the following: (i) The coordinates of B. (ii) The coordinates of C. (iii) The point identified by the coordinates (–3, –5) (iv) The point identified by the coordinates (2, –4) (v) The abscissa of the point D. (vi) The ordinate of the point H. (vii) The coordinates of the point L. (viii) The coordinates of the point M.
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Additional Practice Questions
What are the coordinates of a point located 2 units left and 5 units up from the origin?
easyAnswer: The coordinates are (-2, 5).
Identify the quadrant of the point (-4, 3).
easyAnswer: The point (-4, 3) is located in the second quadrant.
A point moves 3 units down from (4, -1). What are the new coordinates?
mediumAnswer: The new coordinates are (4, -4).
If a point is reflected over the x-axis, how are its coordinates (7, -2) affected?
mediumAnswer: The coordinates become (7, 2) after reflection over the x-axis.
Describe the process of finding the coordinates of a point given its perpendicular distances from the axes.
hardAnswer: Draw perpendicular lines from the point to both axes. The distance from the y-axis gives the x-coordinate (abscissa), and the distance from the x-axis gives the y-coordinate (ordinate). Represent these as (x, y).
How can one determine whether point P is equidistant from the x-axis and y-axis if its coordinates are unknown?
hardAnswer: Point P is equidistant from the x-axis and y-axis if the absolute values of its x-coordinate and y-coordinate are equal, i.e., if |x| = |y|.