Revision: Coordinate Geometry Basics MCQs Quiz | Class 10
This quiz covers important concepts from Class X Mathematics (Code 041), specifically Unit III: Coordinate Geometry. It focuses on Revision: Coordinate Geometry Basics MCQs, including topics such as Quadrants, plotting points, and graphs of linear equations. Test your knowledge, submit your answers to see your score, and download a detailed answer PDF for review.
Understanding Coordinate Geometry Basics
Coordinate Geometry is a branch of mathematics that uses a coordinate system to study geometry. It provides a connection between algebra and geometry through graphs of lines and curves. In Class X, fundamental concepts like plotting points, understanding quadrants, and drawing graphs of linear equations are crucial.
1. The Cartesian System
The Cartesian system, also known as the coordinate plane, consists of two perpendicular number lines: the horizontal X-axis and the vertical Y-axis. They intersect at a point called the Origin (0,0).
- X-axis: Represents horizontal distances. Positive numbers are to the right of the origin, negative to the left.
- Y-axis: Represents vertical distances. Positive numbers are above the origin, negative below.
- Quadrants: The axes divide the plane into four regions called quadrants.
- First Quadrant (I): x greater than 0, y greater than 0 (e.g., (3, 5))
- Second Quadrant (II): x less than 0, y greater than 0 (e.g., (-2, 4))
- Third Quadrant (III): x less than 0, y less than 0 (e.g., (-6, -1))
- Fourth Quadrant (IV): x greater than 0, y less than 0 (e.g., (7, -3))
- Coordinates: A point in the plane is represented by an ordered pair (x, y), where ‘x’ is the abscissa (distance from Y-axis) and ‘y’ is the ordinate (distance from X-axis).
2. Plotting Points
To plot a point (x, y):
- Start at the origin (0,0).
- Move ‘x’ units horizontally (right if x is positive, left if x is negative).
- From that position, move ‘y’ units vertically (up if y is positive, down if y is negative).
Example: To plot (2, 3), move 2 units right from origin, then 3 units up. To plot (-1, -4), move 1 unit left from origin, then 4 units down.
3. Graphs of Linear Equations
A linear equation in two variables (like Ax + By + C = 0 or y = mx + c) always represents a straight line when plotted on the Cartesian plane. Every point (x, y) that satisfies the equation lies on this line.
To draw the graph of a linear equation:
- Find at least two (preferably three) pairs of (x, y) values that satisfy the equation.
- Plot these points on the coordinate plane.
- Draw a straight line passing through these points.
Example: For the equation y = x + 2
| x | y = x + 2 | Point (x, y) |
|---|---|---|
| 0 | 2 | (0, 2) |
| 1 | 3 | (1, 3) |
| -2 | 0 | (-2, 0) |
Plot (0,2), (1,3), and (-2,0) and draw a line through them.
Quick Revision Points:
- The X-axis equation is y = 0.
- The Y-axis equation is x = 0.
- The origin is (0,0).
- Points on the X-axis have the form (x, 0).
- Points on the Y-axis have the form (0, y).
- The Distance Formula: Distance between P(x1, y1) and Q(x2, y2) is sqrt((x2 – x1)^2 + (y2 – y1)^2).
- The Section Formula: Coordinates of a point P(x, y) dividing the line segment joining A(x1, y1) and B(x2, y2) internally in the ratio m1 : m2 are ((m1*x2 + m2*x1)/(m1 + m2), (m1*y2 + m2*y1)/(m1 + m2)).
Practice More:
Try answering these questions to reinforce your understanding:
- Find the coordinates of a point that is 3 units to the left of the Y-axis and 5 units above the X-axis.
- A point (k, -k) for k greater than 0 lies in which quadrant?
- Write the equation of a line parallel to the Y-axis at a distance of 4 units to its right.
- Determine if the point (2, 5) lies on the line given by the equation y = 3x – 1.
- What is the distance between the points (6, 0) and (0, -8)?
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