RBSE Solutions Class 8 Maths Chapter 12 Linear Graph Exercise 12.1

Exercise 12.1

Question 1. Fill in the blanks by seeing the graph 12.5 given below :
(i) Distance from x-axis of a point M is___unit
(ii) Distance from y-axis of a point M is___unit
(iii) Distance from y-axis of a point N is___unit
(iv) Point T is plotted on quadrant___
(v) Distance from x-axis of a point T is___unit

Answer:
(i) 3
(ii) 2
(iii) 3
(iv) fourth
(v) 4
In simple words: Look at the graph to find the location of each point. The distance from the x-axis is the absolute value of the y-coordinate, and the distance from the y-axis is the absolute value of the x-coordinate. The quadrant is determined by the signs of the x and y coordinates.

🎯 Exam Tip: Always remember that the distance from an axis is always a positive value, even if the coordinate is negative.

Question 2. Abscissa and ordinate are of point P. Therefore, the coordinates of point P are___. Abscissa and ordinate are of point Q. Therefore, the coordinates of point Q are___. x-coordinate and y-coordinate are of point R. Therefore, the coordinates of point R are___. x-coordinate and y-coordinate are of point S. Therefore, the coordinates of point S are___.

Answer:
(i) 2, 1, (2, 1)
(ii) -3, 2, (-3, 2)
(iii) -4, -3, (-4, -3)
(iv) 3, -2, (3, -2)
In simple words: Find the horizontal value (x-coordinate or abscissa) and the vertical value (y-coordinate or ordinate) for each point on the graph. Write them together as a pair (x, y) to show the point's exact location.

🎯 Exam Tip: Always write the x-coordinate first and then the y-coordinate in a pair (x, y) when stating point coordinates.

Question 3. Plot the following points on squared paper and check whether they all are situated on straight line.
(i) A(1, 1); B(1, 2); C(1, 3); D(1, 4)
Answer:

Yes, all points A(1, 1), B(1, 2), C(1, 3), D(1, 4) are situated on a straight line. They form a vertical line.
In simple words: Plot each point on the graph. If they all fall on a single straight line when connected, then they are collinear. In this case, all points lie on the line \( x=1 \), so they are on a straight line.

🎯 Exam Tip: Points with the same x-coordinate always lie on a vertical straight line, and points with the same y-coordinate always lie on a horizontal straight line.

(ii) K(1, 3); L(5, 3); M(5, 5); N(1, 5)
Answer:

No, all points K(1, 3), L(5, 3), M(5, 5), N(1, 5) are not situated on a straight line. They form a rectangle.
In simple words: Plot the given points on the graph. If they cannot all be connected by a single straight line, they are not collinear. These points form the corners of a rectangle, not a line.

🎯 Exam Tip: Plotting points carefully helps determine if they are collinear or form a specific shape. Visual inspection is a key part of such problems.

(iii) P(2, 6); Q(5, 5); Y(5, 3); Z(6, 3)
Answer:

No, all points P(2, 6), Q(5, 5), Y(5, 3), Z(6, 3) are not situated on a straight line. They do not form a single straight line when connected.
In simple words: When you plot these points, you can see that they do not all lie on the same straight path. This means they are not collinear.

🎯 Exam Tip: To check for collinearity, try to draw a single straight line through all the points. If it's not possible, they are not collinear.

Question 4. Draw the following graph 12.7 on graph paper, write the answer of the questions given below.
(i) Write the coordinates of vertices of parallelogram ABCD. Find the length of sides AB and DC.
(ii) Find the coordinates of vertices of triangle PQR also find the length of base PQ.
Answer:

Answer:
(i) The coordinates of the vertices of parallelogram ABCD are:
A \( \to \) (1, 5)
B \( \to \) (5, 5)
C \( \to \) (6, 8)
D \( \to \) (2, 8)
Length of side AB = \( |5 - 1| = 4 \) units.
Length of side DC = \( |6 - 2| = 4 \) units. Since AB and DC are parallel to the x-axis, their length is the difference in x-coordinates.

(ii) The coordinates of the vertices of triangle PQR are:
P \( \to \) (1, 1)
Q \( \to \) (4, 1)
R \( \to \) (1, 3)
Length of base PQ = \( |4 - 1| = 3 \) units. Since PQ is parallel to the x-axis, its length is the difference in x-coordinates.
In simple words: To find the coordinates of a point, look at its x and y values on the graph. To find the length of a horizontal line segment, count the units between its x-coordinates. For a vertical line, count the units between its y-coordinates.

🎯 Exam Tip: Always check if sides are horizontal or vertical when calculating lengths; if not, use the distance formula. For coordinates, remember (x, y).

Question 5. Write the true or false in front of each statements-
(i) Location of a point on graph paper is represented by the number pair.
(ii) Linear graph shows the change in data with respect to time interval.
(iii) Point having x-coordinate zero and y- coordinate non-zero, is located on y-axis.
(iv) Point having y-coordinate zero and x- coordinate 5, well be located on y-axis.
(v) Coordinates of origin are (1, 1).
Answer:
(i) True
(ii) True
(iii) True
(iv) False
(v) False.
In simple words: A point's location on a graph is always shown by two numbers, an x and a y. Linear graphs are good for showing how things change over time. If a point's x-value is zero but its y-value is not, it sits on the y-axis. If a point's y-value is zero and its x-value is 5, it sits on the x-axis (not the y-axis). The starting point (origin) is always (0,0), not (1,1).

🎯 Exam Tip: Understand the definitions of coordinates, axes, and the origin. A common mistake is confusing the x and y axes for points where one coordinate is zero.