Page 1 Exercise 10.1 page: 10.7 1. Make three points in your notebook and name them. Solution: The three points A, P and H are marked as given below: 2. Draw a line in your notebook and name it using a small letter of the alphabet. Solution: The line AB is drawn and is named as l 3. Draw a line in your notebook and name it by taking any two points on it. Solution: Construct a line and name the points PQ. It can be called as the line PQ. 4. Give three examples from your environment of: (i) Points (ii) Portion of a line (iii) Plane surfaces (iv) Portion of a plane (v) Curved surfaces Solution: (i) Points The three examples are Pinhole on the map Two walls and floor meeting at the corner Period at the end of the sentence (ii) Portion of a line Page 2 Exercise 10.1 page: 10.7 1. Make three points in your notebook and name them. Solution: The three points A, P and H are marked as given below: 2. Draw a line in your notebook and name it using a small letter of the alphabet. Solution: The line AB is drawn and is named as l 3. Draw a line in your notebook and name it by taking any two points on it. Solution: Construct a line and name the points PQ. It can be called as the line PQ. 4. Give three examples from your environment of: (i) Points (ii) Portion of a line (iii) Plane surfaces (iv) Portion of a plane (v) Curved surfaces Solution: (i) Points The three examples are Pinhole on the map Two walls and floor meeting at the corner Period at the end of the sentence (ii) Portion of a line The three examples are Thin curtain rods Laser beams Stretched power cables (iii) Plane surfaces The three examples are Surface of a white board Top of a table Surface of a wall (iv) Portion of a plane The three examples are Surface of a mirror Calm water in a swimming pool Surface of the sheet of paper (v) Curved surfaces The three examples are Ink pot Tea pot Gas cylinder 5. There are a number of ways by which we can visualise a portion of a line. State whether the following represent a portion of a line or not: (i) A piece of elastic stretched to the breaking point. (ii) Wire between two electric poles. (iii) The line thread by which a spider lowers itself. Solution: (i) Yes. (ii) No. (iii) Yes. 6. Can you draw a line on the surface of a sphere which lies wholly on it? Solution: No. A line cannot be drawn on the surface of the sphere which lies wholly on it. 7. Mark a point on a sheet of paper and draw a line passing through it. How many lines can you draw through this point? Solution: Unlimited number of lines can be drawn through the point L. Page 3 Exercise 10.1 page: 10.7 1. Make three points in your notebook and name them. Solution: The three points A, P and H are marked as given below: 2. Draw a line in your notebook and name it using a small letter of the alphabet. Solution: The line AB is drawn and is named as l 3. Draw a line in your notebook and name it by taking any two points on it. Solution: Construct a line and name the points PQ. It can be called as the line PQ. 4. Give three examples from your environment of: (i) Points (ii) Portion of a line (iii) Plane surfaces (iv) Portion of a plane (v) Curved surfaces Solution: (i) Points The three examples are Pinhole on the map Two walls and floor meeting at the corner Period at the end of the sentence (ii) Portion of a line The three examples are Thin curtain rods Laser beams Stretched power cables (iii) Plane surfaces The three examples are Surface of a white board Top of a table Surface of a wall (iv) Portion of a plane The three examples are Surface of a mirror Calm water in a swimming pool Surface of the sheet of paper (v) Curved surfaces The three examples are Ink pot Tea pot Gas cylinder 5. There are a number of ways by which we can visualise a portion of a line. State whether the following represent a portion of a line or not: (i) A piece of elastic stretched to the breaking point. (ii) Wire between two electric poles. (iii) The line thread by which a spider lowers itself. Solution: (i) Yes. (ii) No. (iii) Yes. 6. Can you draw a line on the surface of a sphere which lies wholly on it? Solution: No. A line cannot be drawn on the surface of the sphere which lies wholly on it. 7. Mark a point on a sheet of paper and draw a line passing through it. How many lines can you draw through this point? Solution: Unlimited number of lines can be drawn through the point L. 8. Mark any two points P and Q in your note book and draw a line passing through the points. How many lines can you draw passing through both the points? Solution: Draw a line passing through the points P and Q Only one line can be drawn passing through this both points. 9. Give an example of a horizontal plane and a vertical plane from your environment. Solution: The example of horizontal plane is ceiling of a room. The example of a vertical plane is wall of a room. 10. How many lines may pass through one given point, two given points, any three collinear points? Solution: The lines passing through one given point is unlimited. The lines passing through two given points are only one. Page 4 Exercise 10.1 page: 10.7 1. Make three points in your notebook and name them. Solution: The three points A, P and H are marked as given below: 2. Draw a line in your notebook and name it using a small letter of the alphabet. Solution: The line AB is drawn and is named as l 3. Draw a line in your notebook and name it by taking any two points on it. Solution: Construct a line and name the points PQ. It can be called as the line PQ. 4. Give three examples from your environment of: (i) Points (ii) Portion of a line (iii) Plane surfaces (iv) Portion of a plane (v) Curved surfaces Solution: (i) Points The three examples are Pinhole on the map Two walls and floor meeting at the corner Period at the end of the sentence (ii) Portion of a line The three examples are Thin curtain rods Laser beams Stretched power cables (iii) Plane surfaces The three examples are Surface of a white board Top of a table Surface of a wall (iv) Portion of a plane The three examples are Surface of a mirror Calm water in a swimming pool Surface of the sheet of paper (v) Curved surfaces The three examples are Ink pot Tea pot Gas cylinder 5. There are a number of ways by which we can visualise a portion of a line. State whether the following represent a portion of a line or not: (i) A piece of elastic stretched to the breaking point. (ii) Wire between two electric poles. (iii) The line thread by which a spider lowers itself. Solution: (i) Yes. (ii) No. (iii) Yes. 6. Can you draw a line on the surface of a sphere which lies wholly on it? Solution: No. A line cannot be drawn on the surface of the sphere which lies wholly on it. 7. Mark a point on a sheet of paper and draw a line passing through it. How many lines can you draw through this point? Solution: Unlimited number of lines can be drawn through the point L. 8. Mark any two points P and Q in your note book and draw a line passing through the points. How many lines can you draw passing through both the points? Solution: Draw a line passing through the points P and Q Only one line can be drawn passing through this both points. 9. Give an example of a horizontal plane and a vertical plane from your environment. Solution: The example of horizontal plane is ceiling of a room. The example of a vertical plane is wall of a room. 10. How many lines may pass through one given point, two given points, any three collinear points? Solution: The lines passing through one given point is unlimited. The lines passing through two given points are only one. The lines passing through three collinear points are one. 11. Is it ever possible for exactly one line to pass through three points? Solution: Yes. It is possible for a line to pass through three points, if the points lie on a straight line. 12. Explain why it is not possible for a line to have a mid-point. Solution: We know that the length of the line is infinite and it is not possible to find the midpoint. But it is possible to find the midpoint of line segments. 13. Mark three non-collinear points A, B and C in your note book. Draw lines through these points taking two at a time. Name these lines. How many such different lines can be drawn? Solution: It is given that the three collinear points are A, B and C We know that three lines namely AB, BC and AC can be drawn using these points. Page 5 Exercise 10.1 page: 10.7 1. Make three points in your notebook and name them. Solution: The three points A, P and H are marked as given below: 2. Draw a line in your notebook and name it using a small letter of the alphabet. Solution: The line AB is drawn and is named as l 3. Draw a line in your notebook and name it by taking any two points on it. Solution: Construct a line and name the points PQ. It can be called as the line PQ. 4. Give three examples from your environment of: (i) Points (ii) Portion of a line (iii) Plane surfaces (iv) Portion of a plane (v) Curved surfaces Solution: (i) Points The three examples are Pinhole on the map Two walls and floor meeting at the corner Period at the end of the sentence (ii) Portion of a line The three examples are Thin curtain rods Laser beams Stretched power cables (iii) Plane surfaces The three examples are Surface of a white board Top of a table Surface of a wall (iv) Portion of a plane The three examples are Surface of a mirror Calm water in a swimming pool Surface of the sheet of paper (v) Curved surfaces The three examples are Ink pot Tea pot Gas cylinder 5. There are a number of ways by which we can visualise a portion of a line. State whether the following represent a portion of a line or not: (i) A piece of elastic stretched to the breaking point. (ii) Wire between two electric poles. (iii) The line thread by which a spider lowers itself. Solution: (i) Yes. (ii) No. (iii) Yes. 6. Can you draw a line on the surface of a sphere which lies wholly on it? Solution: No. A line cannot be drawn on the surface of the sphere which lies wholly on it. 7. Mark a point on a sheet of paper and draw a line passing through it. How many lines can you draw through this point? Solution: Unlimited number of lines can be drawn through the point L. 8. Mark any two points P and Q in your note book and draw a line passing through the points. How many lines can you draw passing through both the points? Solution: Draw a line passing through the points P and Q Only one line can be drawn passing through this both points. 9. Give an example of a horizontal plane and a vertical plane from your environment. Solution: The example of horizontal plane is ceiling of a room. The example of a vertical plane is wall of a room. 10. How many lines may pass through one given point, two given points, any three collinear points? Solution: The lines passing through one given point is unlimited. The lines passing through two given points are only one. The lines passing through three collinear points are one. 11. Is it ever possible for exactly one line to pass through three points? Solution: Yes. It is possible for a line to pass through three points, if the points lie on a straight line. 12. Explain why it is not possible for a line to have a mid-point. Solution: We know that the length of the line is infinite and it is not possible to find the midpoint. But it is possible to find the midpoint of line segments. 13. Mark three non-collinear points A, B and C in your note book. Draw lines through these points taking two at a time. Name these lines. How many such different lines can be drawn? Solution: It is given that the three collinear points are A, B and C We know that three lines namely AB, BC and AC can be drawn using these points. 14. Coplanar points are the points that are in the same plane. Thus, (i) Can 150 points be coplanar? (ii) Can 3 points be non-coplanar? Solution: (i) Yes. We know that the group of points which lie in the same plane are coplanar points. Hence, 150 points can be coplanar. (ii) No. We know that 3 points can be coplanar as we can have plane which contains 3 points. Hence, 3 points cannot be non-coplanar. 15. Using a ruler, check whether the following points given in Fig. 10.30 are collinear or not: (i) D, A and C (ii) A, B and C (iii) A, B and E (iv) B, C and E Solution: (i) The points D, A and C are collinear. (ii) The points A, B and C are non-collinear. (iii) The points A, B and E are collinear. (iv) The points B, C and E are non-collinear. 16. Lines p, q are coplanar. So are the lines p, r. Can we conclude that the lines p, q, r are coplanar? Solution:Read More

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