RD Sharma Class 8 Solutions Chapter 27 - Introduction to Graphs (Ex 27.1) Exercise 27.1 - Free PDF
FAQs on RD Sharma Class 8 Solutions Chapter 27 - Introduction to Graphs (Ex 27.1) Exercise 27.1
1. What is the correct step-by-step method to plot a point, for example, P(4, 3), as required in the RD Sharma solutions for Exercise 27.1?
To plot a point like P(4, 3) on a graph, follow these steps as per the method used in RD Sharma solutions:
Start at the origin (0,0), which is the intersection of the x-axis and y-axis.
Move 4 units to the right along the horizontal x-axis, as the x-coordinate is positive 4.
From that position, move 3 units up, parallel to the vertical y-axis, as the y-coordinate is positive 3.
Mark this final point as P. This location correctly represents the coordinates (4, 3).
2. How do you identify the coordinates of a point that is already plotted on a graph in Chapter 27?
To find the coordinates of a given point on a graph, you must determine its distance from both axes:
To find the x-coordinate (abscissa), draw a perpendicular line from the point down to the x-axis. The value where this line meets the x-axis is your x-coordinate.
To find the y-coordinate (ordinate), draw a perpendicular line from the point across to the y-axis. The value where this line meets the y-axis is your y-coordinate.
Always write the coordinates in the format (x, y).
3. What is a common mistake when plotting points with a zero coordinate, like (5, 0) or (0, 3), and how can it be avoided?
A common mistake is placing the point in the wrong dimension. To avoid this, remember:
A point with a zero y-coordinate, such as (5, 0), has no vertical distance from the x-axis. Therefore, it will always lie directly on the x-axis.
A point with a zero x-coordinate, such as (0, 3), has no horizontal distance from the y-axis. Therefore, it will always lie directly on the y-axis.
Never plot a point like (5, 0) at the origin; its location is determined by the non-zero value.
4. Why are the points (5, 2) and (2, 5) considered different when solving problems in this exercise?
The points (5, 2) and (2, 5) are different because the order of coordinates matters in the Cartesian system. The first number always represents the horizontal position (x-axis) and the second represents the vertical position (y-axis).
For (5, 2), you move 5 units right and 2 units up.
For (2, 5), you move 2 units right and 5 units up.
Swapping the numbers changes the point's location entirely, which is why correctly identifying the abscissa (x) and ordinate (y) is crucial for an accurate solution.
5. How are the four quadrants of a graph used to verify the position of a plotted point?
The two axes divide the plane into four quadrants. Knowing the sign of the coordinates helps verify if a point is in the correct quadrant, which is a useful checking method for your answers:
Quadrant I: Both x and y are positive (+, +).
Quadrant II: x is negative and y is positive (-, +).
Quadrant III: Both x and y are negative (-, -).
Quadrant IV: x is positive and y is negative (+, -).
If you plot a point like (-3, 4), you can quickly confirm it should be in Quadrant II.
6. After plotting all the points for a question in Exercise 27.1, how can you determine if they form a straight line?
After accurately plotting all the given points on the graph, you can check if they are collinear (lie on the same straight line) by using a ruler. Place the edge of the ruler on the graph and try to connect the points. If all the points lie perfectly along the straight edge of the ruler without any deviation, they form a straight line. This is a practical introduction to the concept of linear graphs which is a key topic in this chapter.
7. What is the significance of the origin (0,0) when solving problems in RD Sharma Exercise 27.1?
The origin (0,0) is the fundamental reference point for all measurements on the Cartesian plane. Every coordinate is measured as a distance from the origin along the axes. When plotting any point (x, y), your first conceptual step is always to start at the origin before moving horizontally and then vertically. Without the origin as a fixed starting point, it would be impossible to plot points at unique and absolute locations.
