Class 9 Coordinate Geometry

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ID : in-9-coordinate-geometry [1] Class 9 Coordinate Geometry For more such worksheets visit www.edugain.com Answer the questions (1) Find the coordinates of the point shown in the picture.

1 ID : in-9-coordinate-geometry [1] Class 9 Coordinate Geometry For more such worksheets visit Answer the questions (1) Find the coordinates of the point shown in the picture. (2) Find the distance of the point (-6, -2) from y-axis. (3) Which of the points W(6, 0), X(0, 16), Y(7, 0) and Z(0, -15) lie on the x-axis? (4) Find the coordinate of the point whose abscissa is 9 and lies on x-axis. (5) Vinayak and Radha deposit some amount in a joint bank account such that total balance remains 800. If amount deposited by Vinayak and Radha are plotted as a linear graph on xy plane, find the area between this graph and the coordinate axis. (6) Find the resultant shape obtained by connecting the points (-30, -20), (-30, 5), (-20, 5) and (-20, -20).

2 (7) Find the coordinates of the point shown in the picture. ID : in-9-coordinate-geometry [2]

3 (8) If coordinates of the point shown in the picture are (p+25, p+30), find the value of p. ID : in-9-coordinate-geometry [3] (9) Find the coordinates of the point which lies on the y-axis at a distance of 9 units from origin in the negative direction of y-axis. (10) Point (-8, 1) lies in which quadrant? Choose correct answer(s) from the given choices (11) A point whose abscissa and ordinate are both negative will lie in the: a. Fourth quadrant b. First quadrant c. Third quadrant d. Second quadrant (12) Signs of the abscissa and ordinate of a point in the third quadrant are: a. -, + b. +, + c. +, - d. -, - (13) Two distinct points in a plane determine line. a. three b. one unique c. two d. infinite (14) The point in which the abscissa and the ordinate have same sign will lie in: a. First or Third quadrant b. Second or Fourth quadrant c. Third or Fourth quadrant d. Second or Third quadrant

4 ID : in-9-coordinate-geometry [4] (15) Two distinct in a plane can not have more than one point in common. a. both lines and points b. planes c. lines d. points 2017 Edugain ( All Rights Reserved Many more such worksheets can be generated at

5 Answers ID : in-9-coordinate-geometry [5] (1) (-20, 20) In order to find the coordinates of the point shown in the picture, let us draw a horizontal and a vertical line that connects this point to the y-axis and x-axis respectively. We can see that the vertical line intersects the x-axis at -20. Therefore, the x-coordinate of the point is -20. Similarly, the horizontal line intersects the y-axis at 20. Therefore, the y-coordinate of the point is 20. Step 4 Hence, the coordinates of the given point are (-20, 20).

6 (2) 6 ID : in-9-coordinate-geometry [6] The simplest way to solve it is to remember that the abscissa is the position "on" the x-axis, and the ordinate is the position "on" the y-axis. This means that the first value is the distance of the point from the y-axis, and the ordinate is the distance of the point from the x-axis. Also remember to remove the negative sign as the distance is always positive. We have to find the distance of the given point (-6, -2) from y-axis, which will be equal to the abscissa of the point (ignoring the negative sign),i.e., 6. (3) Y and W We know that a point lying on the x-axis will have the ordinate as 0 and a point lying on the y-axis will have the abscissa as 0. We can see that out of all the points Y and W have the ordinate zero, which means points Y and W will lie on the x-axis. (4) (9,0) The first value x, of coordinates of any point (x, y) is called the abscissa, and the second value y is called the ordinate. Now, we know that if a point lies on the x-axis then its ordinate is 0. In the given question, since the point lies on x-axis and the value of its abscissa is 9, the coordinates of the point will be (9,0).

7 (5) ID : in-9-coordinate-geometry [7] Let the amount deposited by Vinayak be x and by Radha be y. Since the balance remains 800, the relation between x and y will be given by x + y = 800. We know that the area of a triangle is equal to half the product of base and the height. Step 4 The area of the given triangle will be equal to: = sq units.

8 (6) Rectangle ID : in-9-coordinate-geometry [8] Let us plot the given points on a graph paper and join them as shown below: Now, we notice the following: 1. Opposite sides are equal and parallel to each other. 2. All angles are equal and are right angles. These are the properties of a Rectangle. Therefore, the shape obtained on joining these points is a Rectangle.

9 (7) (-1, -3) ID : in-9-coordinate-geometry [9] In order to find the coordinates of the point shown in the picture, let us draw a horizontal and a vertical line which connect this point to the y-axis and x-axis respectively. We can see that the vertical line intersects the x-axis at -1. Therefore, the abscissa of the point is - 1. Similarly, the horizontal line intersects the y-axis at -3. Therefore, the ordinate of the point is -3. Step 4 Hence, the coordinates of the given point are (-1, -3).

10 (8) 5 ID : in-9-coordinate-geometry [10] From observation we see that the point defined is (30,35). It is given that, 30 = p + 25 and 35 = p + 30 or, p = 5 From either of these equations we can see that p = 5. (9) (0, -9) Since the given point lies on the y axis, its abscissa will be equal to zero. The distance of the point from the origin is 9 units in the negative direction. This means that the ordinate of the point will be -9. From above two steps, we can say that the point is (0, -9).

(10) Second quadrant ID : in-9-coordinate-geometry [11] For plotting a point (x, y) on the graph, we have to keep in mind the following points: If both the numbers are positive i.e. (x,y), then the point lies in the first quadrant.

11 (10) Second quadrant ID : in-9-coordinate-geometry [11] For plotting a point (x, y) on the graph, we have to keep in mind the following points: If both the numbers are positive i.e. (x,y), then the point lies in the first quadrant. If the first number is negative, and the second number is positive i.e. (-x,y), it lies in the second quadrant. If both the numbers are negative (-x,-y), it lies in the third quadrant. If the first number is positive and the second number is negative (x,-y), it lies in the fourth quadrant. We can see that for the given point, x is less than zero and y is greater than zero. Hence, the point will lie in the Second quadrant.

(11) c. Third quadrant ID : in-9-coordinate-geometry [12] There is a very simple mental map for this as shown below: We need to go in the anticlockwise direction for this.

12 (11) c. Third quadrant ID : in-9-coordinate-geometry [12] There is a very simple mental map for this as shown below: We need to go in the anticlockwise direction for this. If both the numbers are positive (x,y), then the point lies in the first quadrant. If the first number is negative, and the second is positive (-x,y), it lies in the second quadrant. Step 4 If both numbers are negative (-x,-y), it lies in the third quadrant. Step 5 If the first is positive and the second is negative (x,-y), it lies in the fourth quadrant. Step 6 Here both values are negative, therefore it will lie in the Third quadrant.

13 (12) d. -, - ID : in-9-coordinate-geometry [13] The key to solving such questions is to build a mental map of the quadrants. The quadrants get decided based on the following points: i. When both abscissa and ordinate are positive i.e. (x,y), then the point lies in the first quadrant. (The positioning of next quadrants will be done in anticlockwise direction.) ii. When abscissa is negative and ordinate is positive i.e. (-x,y), it lies in quadrant two. iii. When abscissa and ordinate both are negative i.e. (-x,-y), it lies in quadrant three. iv. When abscissa is positive and ordinate is negative i.e. (x,-y), it lies in quadrant four. (13) b. one unique Following figure shows a line, that is drawn through two distinct points A and B. If we try to draw another line, it will not go through both A and B. Therefore, two distinct points in a plane determine one unique line.

14 (14) a. First or Third quadrant ID : in-9-coordinate-geometry [14] There is a very simple mental map for this. In the first quadrant, both the abscissa and ordinate (x,y) are positive. In the second quadrant, the abscissa is negative, and the ordinate is positive (-x,y). Step 4 In the third quadrant, both the numbers are negative (-x,-y). Step 5 In the fourth quadrant, the abscissa is positive and the ordinate is negative (x,-y). Step 6 Based on this, we find the answer to the question is First or Third quadrant. (15) c. lines Following figure shows the lines AB and CD, intersected at the point E. From the given figure it is clear that, the two distinct lines can intersect at a single point only and hence, we can say that the two distinct lines in a plane can not have more than one point in common.

CO-ORDINATE GEOMETRY CHAPTER 3. Points to Remember :

CO-ORDINATE GEOMETRY CHAPTER 3. Points to Remember : CHAPTER Points to Remember : CO-ORDINATE GEOMETRY 1. Coordinate axes : Two mutually perpendicular lines X OX and YOY known as x-axis and y-axis respectively, constitutes to form a co-ordinate axes system.