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 t he quest ions (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 t he quest ions (1) Find the coordinates of the point shown in the picture. (2) Find the coordinates of points which lies on y-axis at a distance of 7 units f rom origin in the positive direction of y-axis. (3) Find the coordinate of point whose abscissa is 5 and which lies on x-axis. (4) Find the distance of point (7, 4) f rom x-axis. Choose correct answer(s) f rom given choice (5) Which of the points J(12, 0), K(-10, 0), L(0, 14) and M(0, 14) lie on y axis. a. M and L b. L and J c. K and J d. M and K

(2) Find the coordinates of points which lies on y-axis at a distance of 7 units f rom origin in the positive direction of y-axis.

2 ID : in-9-coordinate-geometry [2] (6) Find the resultant shape obtained by connecting points (15, 25) (-10, 25) (0, 5) and (-25, 5). a. Square b. Rectangle c. Parallelogram d. Rhombus (7) Two distinct points in a plane determine line. a. Three b. Two c. Inf inite d. One unique (8) The points in which abscissa and ordinate have same sign will lie in a. Second and T hird quadrants b. First and Fourth quadrants c. First and T hird quadrants d. Second and Fourth quadrants (9) Point (6, 5) lies in which quadrant? a. Second quadrant b. Fourth quadrant c. First quadrant d. T hird quadrant (10) Find the coordinates of the point shown in the picture. a. (4, 3) b. (40, 30) c. (30, 40) d. (3, 4)

One unique (8) The points in which abscissa and ordinate have same sign will lie in a. Second and T hird quadrants b. First and Fourth quadrants c.

3 (11) If coordinates of the point shown in the picture are (p+35, p+15), f ind the value of p. ID : in-9-coordinate-geometry [3] a. -60 b. -40 c. -45 d. -50 (12) A point both of whose coordinates are negative will lie in a. Second quadrant b. T hird quadrant c. Fourth quadrant d. First quadrant (13) Signs of the abscissa and ordinate of a point in the second quadrant are respectively a. -, + b. +, + c. -, - d. +, - (14) Two distinct in a plane can not have more than one point in common. a. Planes b. Both lines and points c. Lines d. Points Fill in the blanks (15) Pranav and Ashish deposit some amount in joint back account such that total balance remains If amount deposited by Pranav and Ashish are plotted as linear graph on x-y plane, the area between this graph and coordinate axes =.

First quadrant (13) Signs of the abscissa and ordinate of a point in the second quadrant are respectively a. -, + b. +, + c. -, - d.

5 Answers ID : in-9-coordinate-geometry [5] (1) (-4, 2.5) In order to f ind the coordinates of the point shown in the picture, let's draw a horizontal and a vertical line which connect this point to the y and x axis respectively. We can see that the vertical line intersects the x-axis at -4. Theref ore, the x-coordinate of the point is -4. Step 3 Similarly, the horizontal line intersects the y-axis at 2.5. T heref ore, the y-coordinate of the point is 2.5. Step 4 Hence the coordinates of the given point are (-4, 2.5) (2) (0, 7) Note that if the point lies on the y-axis, then the x coordinate will be 0. The value of the y coordinate will be 7 if it lies in the positive direction, and -7 if it lies in the negative direction.

We can see that the vertical line intersects the x-axis at -4. Theref ore, the x-coordinate of the point is -4. Step 3 Similarly, the horizontal line intersects the y-axis at 2.5.

6 (3) (5,0) ID : in-9-coordinate-geometry [6] The key to note is that the f irst value that represents a point is called the abscissa, and the second value is called the ordinate. The second point to remember is that if a point lies on the x-axis, then the ordinate value is 0. Here we are given the abscissa value, and told that the point lies on the x axis, so the answer is (5,0) (4) 4 The simplest way to solve it is to remember that the abscissa - the f irst value - is the position "on" the x axis, and the ordinate is the value "on" the y axis What this means is that the f irst value is the distance away f rom the y axis, and the ordinate is the distance away f rom the x axis. Also remember to remove the sign - the distance is always positive (5) a. M and L A point lying on the X axis will have the abscissa as 0, and a point lying on the Y axis will have the ordinate as 0. Looking at the points here, we see points M and L will theref ore lies on the y axis

Here we are given the abscissa value, and told that the point lies on the x axis, so the answer is (5,0) (4) 4 The simplest way to solve it is to remember that the abscissa - the f irst value - is

7 (6) d. Rhombus ID : in-9-coordinate-geometry [7] We can draw these points and connect them on graph paper as f ollowing Now we notice f ollowing in this shape, 1. All sides are equal 2. Opposite sides are parallel to each other Step 3 These are the properties of Rhombus, theref ore this shape is a Rhombus

8 (7) d. One unique ID : in-9-coordinate-geometry [8] Following f igure 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. Theref ore only one line can be drawn through two points (8) c. First and T hird quadrants There is a very simple mental map f or this. In the f irst 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). In the third quadrant, both numbers are negative (-x,-y). In the f ourth quadrant, the abscissa is positive and the ordinate is negative (-x,-y). Based on this, we f ind the answer to the question is First and Third quadrants

First and T hird quadrants There is a very simple mental map f or this. In the f irst quadrant, both the abscissa and ordinate (x,y) are positive.

(9) c. First quadrant ID : in-9-coordinate-geometry [9] There is a very simple mental map f or this. You need to go in the anticlockwise direction f or this. If both the numbers are positive (i.e. in the f orm (x,y), then the point lies in the f irst quadrant.

9 (9) c. First quadrant ID : in-9-coordinate-geometry [9] There is a very simple mental map f or this. You need to go in the anticlockwise direction f or this. If both the numbers are positive (i.e. in the f orm (x,y), then the point lies in the f irst quadrant. If the f irst number is negative, and the second is positive (-x,y), it lies in the second quadrant. If both numbers are negative (-x,-y), it lies in the 3rd quadrant. If the f irst is positive and the second is negative (x,-y), it lies in the 4th quadrant. Here the f irst number is positive, and the second is positive, so it lies in the First quadrant.

If the f irst number is negative, and the second is positive (-x,y), it lies in the second quadrant.

10 (10) b. (40, 30) ID : in-9-coordinate-geometry [10] In order to f ind the coordinates of the point shown in the picture, let's draw a horizontal and a vertical line which connect this point to the y and x axis respectively. We can see that the vertical line intersects the x-axis at 40. Theref ore, the x-coordinate of the point is 40. Step 3 Similarly, the horizontal line intersects the y-axis at 30. T heref ore, the y-coordinate of the point is 30. Step 4 Hence the coordinates of the given point are (40, 30). (11) d. -50 From observation we see that the point def ined is (-15,-35) We are told that -15 = p + 35, and -35 = p + 15 From either of these equations we can see that p = -50

this point to the y and x axis respectively. We can see that the vertical line intersects the x-axis at 40. Theref ore, the x-coordinate of the point is 40.

11 (12) b. Third quadrant ID : in-9-coordinate-geometry [11] There is a very simple mental map f or this. You need to go in the anticlockwise direction f or this. If both the numbers are positive (x,y), then the point lies in the f irst quadrant. If the f irst number is negative, and the second is positive (-x,y), it lies in the second quadrant. If both numbers are negative (-x,-y), it lies in the 3rd quadrant. If the f irst is positive and the second is negative (x,-y), it lies in the 4th quadrant. Here both values are negative, theref ore it will lie in the Third quadrant (13) a. -, + The key to solving such questions is to build a mental map of the quadrants. When both abscissa and ordinate are positive values (x,y), then the point is in the f irst quadrant. From there we go anticlockwise. When abscissa is negative and ordinate is positive (-x,y), it is in quadrant two. When both are negative (-x,-y), it is quadrant three. When abscissa is positive and ordinate is negative, the point is in quadrant f our (14) c. Lines Following f igure shows the lines AB and CD, intersected at the point E. From the given f igure 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. (15)

If both numbers are negative (-x,-y), it lies in the 3rd quadrant. If the f irst is positive and the second is negative (x,-y), it lies in the 4th quadrant.

Lecture 8 : Coordinate Geometry. The coordinate plane The points on a line can be referenced if we choose an origin and a unit of 20

Lecture 8 : Coordinate Geometry The coordinate plane The points on a line can be referenced if we choose an origin and a unit of 0 distance on the axis and give each point an identity on the corresponding