RBSE Solutions Class 8 Maths Chapter 12 Linear Graph More Ques

Question 1. Looking at the graph 12.3, for the location of the following points, select the proper alphabets.
(i) (2, 1)
(ii) (0, 5)
(iii) (2, 0)
(iv) coordinates of point A
(v) coordinates of point F
Answer:
(i) The point (2, 1) is represented by the alphabet E on the given graph.
(ii) The point (0, 5) is represented by the alphabet B on the given graph.
(iii) The point (2, 0) is represented by the alphabet G on the given graph. Identifying coordinates is a fundamental skill in graphing.
(iv) The coordinates for point A on the graph are (4, 5).
(v) The coordinates for point F on the graph are (6, 0).
In simple words: Look at the grid and find the letter that matches each number pair (x,y), or find the number pair for each letter.

🎯 Exam Tip: Always double-check both the X (horizontal) and Y (vertical) values when reading coordinates from a graph to avoid errors. The first number is always the x-coordinate, and the second is the y-coordinate.

(i) P (0, 2); Q (0, 5); R (0, 6); S (0, 3)
Answer: When these points are plotted on a graph, they all lie on the same straight line, specifically a vertical line on the Y-axis. This means they are collinear. The straight line formed by these points can be named PR.
In simple words: If you put these points on a graph, they will all make one straight line going up and down. So, they are collinear, and we can call the line PR.

🎯 Exam Tip: To check for collinearity, plot the points and visually inspect if a single straight line can pass through all of them. Points with the same x-coordinate or same y-coordinate are always collinear.

(ii) A(1, 1); B(1, 2); C(1, 3); D(1, 4)
Answer: When these points are plotted on a graph, they all share the same x-coordinate, which is 1. This characteristic places them on a vertical straight line at \( x = 1 \), confirming they are collinear. Plotting points correctly is crucial for understanding linear graphs.
In simple words: When you put these points on a graph, they all line up perfectly in a straight vertical line. This means they are collinear.

🎯 Exam Tip: Points with the same x-coordinate always form a vertical line, and points with the same y-coordinate always form a horizontal line. Both types of lines indicate collinearity.

(iii) K(1, 3); L(2, 3); M(3, 3); N(4, 3)
Answer: When these points are plotted on a graph, they all share the same y-coordinate, which is 3. This means they lie on a horizontal straight line at \( y = 3 \), confirming they are collinear. The straight line formed by these points can be named KN.
In simple words: If you plot these points on a graph, they will all sit on one straight, flat line. This means they are collinear, and we can call that line KN.

🎯 Exam Tip: Always observe if any coordinate (x or y) is common among the points, as this often indicates collinearity along a horizontal or vertical line, simplifying the check.

(iv) W(2, 6); X(3, 5); Y(5, 3); Z(6, 2)
Answer: When these points are plotted on a graph, they lie on a single straight line. To confirm mathematically, we can calculate the slope between consecutive pairs of points. The slope between W(2,6) and X(3,5) is \( \frac{5-6}{3-2} = \frac{-1}{1} = -1 \). The slope between X(3,5) and Y(5,3) is \( \frac{3-5}{5-3} = \frac{-2}{2} = -1 \). Since the slopes between all consecutive points are the same, these points are collinear. The straight line formed by these points can be named WZ.
In simple words: When you draw these points on a graph, they form one smooth, straight line. Because of this, they are called collinear. We can call this line WZ.

🎯 Exam Tip: For points that do not share an x or y coordinate, calculate the slope between consecutive pairs of points. If all slopes are identical, the points are collinear, forming a single diagonal line.