GSEB Class 8 Maths Solutions Chapter 15 Introduction to Graphs Exercise 15.2

Question 1. Plot the following points on a graph sheet. Verify if they lie on a line:
(a) A(4, 0), B(4, 2), C(4, 6) and D(4, 2.5)
(b) P(1, 1), Q(2, 2), R(3, 3) and S(4, 4)
(c) K(2, 3), L(5, 3), M(5, 5) and N(2, 5)
Answer: For each case, we draw the x-axis and the y-axis, then plot the specific points.
(a) When we plot points A(4, 0), B(4, 2), C(4, 6), and D(4, 2.5) and connect them, we discover that they all sit on the same straight line.

(b) By plotting points P(1, 1), Q(2, 2), R(3, 3), and S(4, 4) and then joining them, we observe that they also rest on the same straight line.

(c) Upon plotting points K(2, 3), L(5, 3), M(5, 5), and N(2, 5) and then connecting them, we discover that not all of them are on the same line.
In simple words: First, draw lines for the X and Y axes. Then, mark each point given in the question on your graph. After marking, draw a line through the points for each part. Check if all the points for that part lie perfectly on a single straight line or not.

Exam Tip: Always use a ruler and a sharp pencil to plot points and draw lines accurately on a graph sheet. Misaligned points can lead to incorrect conclusions about whether they lie on a straight line.

Question 2. Draw the line passing through (2, 3) and (3, 2). Find the coordinates of the points at which this line meets the x-axis and y-axis?
Answer: By plotting points A(2, 3) and B(3, 2), we create a line connecting them. When this line is extended, it crosses the x-axis at point C(5, 0) and the y-axis at point D(0, 5).
In simple words: Mark the two given points on a graph. Draw a straight line through these points. Then, extend this line until it touches both the X-axis and the Y-axis, and note down the coordinates where it crosses each axis.

Exam Tip: When drawing a line, use a ruler to ensure it is perfectly straight. To find axis intercepts, extend the line until it clearly crosses the x-axis (where y=0) and the y-axis (where x=0).

Question 3. Write the coordinates of the vertices of each of these adjoining figures?
Answer: Here are the coordinates for the first figure:
1. The coordinates are:
O is (0, 0)
A is (2, 0)
B is (2, 3)
C is (0, 3)

2. The coordinates for the second figure are:
P is (4, 3)
Q is (6, 1)
R is (6, 5)
S is (4, 7)

3. The coordinates for the third figure are:
K is (10, 5)
L is (7, 7)
M is (10, 8)
In simple words: For each shape, look at its corners. Read the X-value first (how far right it is), then the Y-value (how far up it is). Write these two numbers together in parentheses like (X, Y) for every corner.

Exam Tip: When finding coordinates, always remember the x-coordinate comes first (horizontal position) and the y-coordinate comes second (vertical position), in the format (x, y).

Question 4. State whether true or false. Correct that are false?
1. A point whose x coordinate is zero and y-coordinate is non-zero will lie on the y-axis.
2. A point whose y coordinate is zero and x-coordinate is 5 will lie on y-axis.
3. The coordinates of the origin are (0, 0).
Answer:
1. True. A point with an x-coordinate of zero and a y-coordinate that isn't zero will always rest on the y-axis.
2. False. A point where the y-coordinate is zero and the x-coordinate is 5 will rest on the y-axis. This statement is false. A point with a y-coordinate of zero and an x-coordinate of 5 will actually sit on the x-axis, not the y-axis.
3. True. The coordinates for the origin point are (0, 0).
In simple words: Read each statement carefully. Decide if it is true or false. If it is false, write down the correct reason why it is false. For example, if a point is on the X-axis, its Y-value is always zero. If it's on the Y-axis, its X-value is always zero.

Exam Tip: Understand the definitions of x-axis, y-axis, and origin clearly. Points on the x-axis have a y-coordinate of 0, and points on the y-axis have an x-coordinate of 0.