Samacheer Kalvi Class 9 Maths Solutions Chapter 5 Coordinate Geometry Exercise 5.1

Tamilnadu Samacheer Kalvi 9th Maths Solutions Chapter 5 Coordinate Geometry Ex 5.1

 

Question 1. Plot the following points in the coordinate system and identify the quadrants P(-7, 6), Q(7, -2), R(-6, -7), S(3, 5) and T(3, 9)
Answer: The points are plotted on the coordinate plane. Each point's location helps us identify which quadrant it falls into based on whether its x and y coordinates are positive or negative.

(i) P(-7, 6) lies in the II quadrant because its x-coordinate (-7) is negative and its y-coordinate (6) is positive.
(ii) Q(7, -2) lies in the IV quadrant because its x-coordinate (7) is positive and its y-coordinate (-2) is negative.
(iii) R(-6, -7) lies in the III quadrant because both its x-coordinate (-6) and y-coordinate (-7) are negative.
(iv) S(3, 5) lies in the I quadrant because both its x-coordinate (3) and y-coordinate (5) are positive.
(v) T(3, 9) lies in the I quadrant because both its x-coordinate (3) and y-coordinate (9) are positive. All points are located based on their signs.
In simple words: When we place each point on the graph, we can see which section (quadrant) it is in. The signs of the x and y numbers tell us which quadrant. For example, if both numbers are positive, the point is in the first section.

🎯 Exam Tip: Remember the sign rules for each quadrant: (+,+) for I, (-,+) for II, (-,-) for III, and (+,-) for IV. Always label the axes and origin on your graph.

 

Question 2. Write down the abscissa and ordinate of the following.
(i) P
(ii) Q
(iii) R
(iv) S
Answer: The abscissa is the x-coordinate, and the ordinate is the y-coordinate of a point. Each point has a unique pair of these coordinates.
(i) P is (-4, 4): The abscissa is -4, and the ordinate is 4.
(ii) Q is (3, 3): The abscissa is 3, and the ordinate is 3.
(iii) R is (4, -2): The abscissa is 4, and the ordinate is -2.
(iv) S is (-5, -3): The abscissa is -5, and the ordinate is -3.
In simple words: For any point (x, y), 'x' is called the abscissa and 'y' is called the ordinate. We simply state these two numbers for each given point.

🎯 Exam Tip: Always remember that the x-coordinate (abscissa) comes first, and the y-coordinate (ordinate) comes second in an ordered pair (x, y).

 

Question 3. Plot the following points in the coordinate plane and join them. What is your conclusion about the resulting figure?
(i) (-5, 3) (-1, 3) (0, 3) (5, 3)
Answer: When these points are plotted and joined, they form a straight line. Since all the y-coordinates are the same (y=3), this line will be parallel to the x-axis.
The resulting figure is a straight line parallel to the x-axis.
In simple words: When you put all these points on the graph and connect them, you get a straight line that goes from left to right, always staying at the same height (y=3), so it's parallel to the bottom line (x-axis).

🎯 Exam Tip: If all points have the same y-coordinate, they will always form a horizontal line parallel to the x-axis. If all points have the same x-coordinate, they will form a vertical line parallel to the y-axis.

Question 3. Plot the following points in the coordinate plane and join them. What is your conclusion about the resulting figure?
(ii) (0, -4) (0, -2) (0, 4) (0, 5)
Answer: When these points are plotted and joined, they form a straight line. Since all the x-coordinates are the same (x=0), this line will lie exactly on the y-axis.
The resulting figure is a straight line on the y-axis.
In simple words: When you mark these points on the graph and connect them, you get a straight line that goes up and down, right on top of the y-axis. This happens because all points have an x-coordinate of zero.

🎯 Exam Tip: Lines with all x-coordinates as 0 lie on the y-axis, and lines with all y-coordinates as 0 lie on the x-axis.

 

Question 4. Plot the following points in the coordinate plane. Join them in order. What type of geometrical shape is formed?
(i) (0, 0) (-4, 0) (-4, -4) (0, -4)
Answer: When these points are plotted and joined in the given order, they form a square. All sides are equal in length, and adjacent sides are perpendicular.
The geometrical shape formed is a square.
In simple words: When you put these points on the graph in order and draw lines between them, you will see a shape with four equal sides and four square corners. This shape is called a square.

🎯 Exam Tip: To identify a square, check if all four sides are equal and if all internal angles are 90 degrees. Plotting accurately helps visualize this.

Question 4. Plot the following points in the coordinate plane. Join them in order. What type of geometrical shape is formed?
(ii) (-3, 3) (2, 3) (-6, -1) (5, -1)
Answer: When these points are plotted and joined in order, they form a trapezium. A trapezium is a quadrilateral with at least one pair of parallel sides. In this case, the top side (between (-3,3) and (2,3)) and the bottom side (between (-6,-1) and (5,-1)) are both horizontal, making them parallel.
The shape of the geometrical figure is a Trapezium.
In simple words: When you mark these four points and connect them in the right order, you will create a four-sided shape. This shape has two sides that are straight and parallel to each other, like railroad tracks, while the other two sides are slanted. This shape is called a trapezium.

🎯 Exam Tip: To identify a trapezium, look for exactly one pair of parallel sides. Remember that squares and rectangles are special types of parallelograms, not typically referred to as trapeziums.