Samacheer Kalvi Class 8 Maths Solutions Chapter 3 Algebra Exercise 3.8

Tamilnadu Samacheer Kalvi 8th Maths Solutions Chapter 3 Algebra Ex 3.8

Question 1. Fill in the blanks:
(i) X- axis and Y-axis intersect at __________.
Answer: Origin (0,0) The point where the X and Y axes meet is called the origin, and its coordinates are always (0,0). This is the fundamental starting point for all measurements on a graph.
In simple words: The X-axis and Y-axis meet at a spot called the Origin, which is at (0,0).

🎯 Exam Tip: Remember that the origin (0,0) is the fixed reference point from which all other points on a Cartesian plane are measured.

Question 1. (ii) The coordinates of the point in third quadrant are always ___________.
Answer: negative In the third quadrant, both the x-coordinate and the y-coordinate are negative numbers. This specific combination of signs helps locate points accurately in that area of the graph.
In simple words: In the third quadrant, both numbers for a point are always negative.

🎯 Exam Tip: Visualize the four quadrants and remember the sign convention for x and y coordinates in each: (+,+), (-,+), (-,-), (+,-).

Question 1. (iii) (0, -5) point lies on __________ axis.
Answer: Y-axis When a point has an x-coordinate of zero, like in (0, -5), it means the point is located directly on the Y-axis. The value of y then tells you its precise position along that axis.
In simple words: If the first number in a point is zero, the point is on the Y-axis.

🎯 Exam Tip: Points on the Y-axis always have an x-coordinate of 0, and points on the X-axis always have a y-coordinate of 0.

Question 1. (iv) The x- coordinate is always __________ on the y-axis.
Answer: Zero Any point located on the y-axis will always have its x-coordinate equal to zero. This is a fundamental property of the Cartesian coordinate system, simplifying how we describe locations on the axis.
In simple words: For any point on the y-axis, its x-value is always zero.

🎯 Exam Tip: Understand that the axes themselves are part of the coordinate system where one of the coordinates is always zero.

Question 1. (v) __________ coordinates are the same for a line parallel to Y-axis.
Answer: X A line that is parallel to the Y-axis will have the same x-coordinate for all its points. This means its equation will be in the form \( x = c \), where \( c \) is a constant, showing it always stays the same distance from the y-axis.
In simple words: For a line that runs next to the Y-axis, all its points will share the same X-number.

🎯 Exam Tip: Lines parallel to the Y-axis have a constant x-value, while lines parallel to the X-axis have a constant y-value.

Question 2. Say True or False:
(i) (-10,20) lies in the second quadrant.
Answer: True In the point (-10, 20), the x-coordinate is negative (-10) and the y-coordinate is positive (20). This specific combination of signs places the point correctly in the second quadrant of the Cartesian plane, which is typically to the upper left.
In simple words: A point with a negative X and positive Y value, like (-10, 20), is always in the second quadrant. So, it's True.

🎯 Exam Tip: Remember that the second quadrant is where x-values are negative and y-values are positive.

Question 2. (ii) (-9, 0) lies on the x-axis.
Answer: True For any point to lie on the x-axis, its y-coordinate must be zero. Since the point (-9, 0) has a y-coordinate of 0, it is indeed located on the x-axis, specifically 9 units to the left of the origin.
In simple words: A point like (-9, 0) means it's on the X-axis because its Y-number is zero. So, it's True.

🎯 Exam Tip: Points on the x-axis always have the form (x, 0), and points on the y-axis always have the form (0, y).

Question 2. (iii) The coordinates of the origin are (1,1).
Answer: False The origin, which is the central point where the x-axis and y-axis cross, always has coordinates (0, 0). The value (1,1) represents a point in the first quadrant, not the origin, as it is one unit right and one unit up.
In simple words: The origin's coordinates are (0,0), not (1,1). So, the statement is False.

🎯 Exam Tip: Be precise about the origin's coordinates (0,0) as it is a foundational concept in graphing and often a common point of error.

Question 3. Find the quadrants without plotting the points on a graph sheet.
(3, -4), (5, 7), (2, 0), (-3, -5), (4, -3), (-7, 2), (-8, 0), (0, 10), (-9, 50).
Answer:
(3, -4): X is positive, Y is negative
\( \implies \) IV Quadrant
(5, 7): X is positive, Y is positive
\( \implies \) I Quadrant
(2, 0): Y is zero
\( \implies \) X-axis
(-3, -5): X is negative, Y is negative
\( \implies \) III Quadrant
(4, -3): X is positive, Y is negative
\( \implies \) IV Quadrant
(-7, 2): X is negative, Y is positive
\( \implies \) II Quadrant
(-8, 0): Y is zero
\( \implies \) X-axis
(0, 10): X is zero
\( \implies \) Y-axis
(-9, 50): X is negative, Y is positive
\( \implies \) II Quadrant
Understanding the signs of the x and y coordinates quickly tells you which quadrant a point belongs to or if it lies directly on an axis. This classification is key to understanding coordinate geometry.
In simple words: We check the plus or minus signs of the two numbers in each point. If both are positive, it's Quadrant I. Negative X and positive Y is Quadrant II. Both negative is Quadrant III. Positive X and negative Y is Quadrant IV. If one number is zero, the point lies on an axis.

🎯 Exam Tip: Master the sign rules for each quadrant: Q1 (+,+), Q2 (-,+), Q3 (-,-), Q4 (+,-). Points with a zero coordinate lie on an axis, not in a quadrant.

Question 4. Plot the following points in a graph sheet.
A(5, 2), B(-7, -3), C(-2, 4), D(-1, -1), E(0, -5), F(2, 0), G(7, -4), H(-4, 0), I(2, 3), J(8, -4), K(0, 7).
Answer: To plot these points, we start from the origin (0,0) on a graph sheet. For each point, the first number tells us to move horizontally (right for positive, left for negative) along the x-axis. The second number tells us to move vertically (up for positive, down for negative) along the y-axis from that horizontal position. A well-drawn graph with labeled points helps visualize these locations. For example, point A(5, 2) means move 5 units right and 2 units up from the origin. All the given points would be marked clearly with their labels on the graph, providing a visual representation of their coordinates.
In simple words: To plot points, start at (0,0). Move right or left for the first number (x), then up or down for the second number (y). Mark each spot with its letter.

🎯 Exam Tip: Always use a sharp pencil and ruler for accurate plotting. Label each point clearly with its letter and coordinates to avoid confusion, especially when there are many points.

Question 5. Use the graph to determine the coordinates where each figure is located.
Answer: We can find the exact location (coordinates) for each figure by carefully looking at the provided graph. For each figure, we first see its position along the horizontal (x) axis, then its position along the vertical (y) axis. For example, if a Star is 3 units right and 2 units up from the center, its coordinates are (3, 2). Reading the graph carefully for each object will give us the following correct coordinates:

🎯 Exam Tip: Always be careful when reading coordinates from a graph, paying close attention to whether the numbers are positive or negative based on their position from the origin, and whether they lie on an axis.