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Plot point Z (5, – 6) on the Cartesian plane. Construct a right-angled triangle IZN and find the lengths of the three sides. (Comment: Answers may differ from person to person.)
After plotting Z (5, –6) in the fourth quadrant, we construct a right-angled triangle using points I (5, 0) on the x-axis and N (0, 0) at the origin. The vertical side IZ has a length of 6 units, and the horizontal side IN is 5 units. Using the Baudhāyana-Pythagoras Theorem, the hypotenuse ZN lengthRead more
After plotting Z (5, –6) in the fourth quadrant, we construct a right-angled triangle using points I (5, 0) on the x-axis and N (0, 0) at the origin. The vertical side IZ has a length of 6 units, and the horizontal side IN is 5 units. Using the Baudhāyana-Pythagoras Theorem, the hypotenuse ZN length is calculated as the square root of (5 squared plus –6 squared), which equals the square root of 61 units.
For Detailed Solutions:
Visit NCERT Solutions for Class 9 Ganita Manjari Chapter 1 Orienting Yourself: The Use of Coordinates Question Answer:
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-1/
See lessConsider the points R (3, 0), A (0, – 2), M (– 5, – 2) and P (– 5, 2). If they are joined in the same order, predict: (i) Two sides of RAMP that are perpendicular to each other. (ii) One side of RAMP that is parallel to one of the axes. (iii) Two points that are mirror images of each other in one axis. Which axis will this be? Now plot the points and verify your predictions.
By analyzing the coordinates, we can predict that: (i) AM is horizontal (y = –2) and MP is vertical (x = –5), making them perpendicular. (ii) Side AM is parallel to the x-axis because its y-coordinates are constant. (iii) Points M(–5, –2) and P(–5, 2) have the same x-value but opposite y-values, makRead more
By analyzing the coordinates, we can predict that: (i) AM is horizontal (y = –2) and MP is vertical (x = –5), making them perpendicular. (ii) Side AM is parallel to the x-axis because its y-coordinates are constant. (iii) Points M(–5, –2) and P(–5, 2) have the same x-value but opposite y-values, making them mirror images across the x-axis. Plotting these points on a Cartesian plane confirms that RAMP forms a quadrilateral with these properties.
For Detailed Solutions:
Visit NCERT Solutions for Class 9 Ganita Manjari Chapter 1 Orienting Yourself: The Use of Coordinates Question Answer:
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-1/
See lessWhat would a system of coordinates be like if we did not have negative numbers? Would this system allow us to locate all the points on a 2-D plane?
A coordinate system without negative numbers would be limited to the "positive" directions (right and up) from the origin. Historically, the formalization of zero and negative numbers by Indian mathematicians like Brahmagupta was essential for creating the modern four-quadrant Cartesian plane. WithoRead more
A coordinate system without negative numbers would be limited to the “positive” directions (right and up) from the origin. Historically, the formalization of zero and negative numbers by Indian mathematicians like Brahmagupta was essential for creating the modern four-quadrant Cartesian plane. Without these negative values, we could only describe points in Quadrant I, meaning most of the infinite 2-D plane would remain unreachable and unlocatable.
For Detailed Solutions:
Visit NCERT Solutions for Class 9 Ganita Manjari Chapter 1 Orienting Yourself: The Use of Coordinates Question Answer:
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-1/
See lessAre the points M (– 3, – 4), A (0, 0) and G (6, 8) on the same straight line? Suggest a method to check this without plotting and joining the points.
To check if points are collinear without plotting, you can use the ratio method. For points passing through the origin A (0, 0), if the ratio of the y-coordinate to the x-coordinate for all other points is equal, they lie on the same straight line. For the point M (–3, –4), the ratio is 4/3 and forRead more
To check if points are collinear without plotting, you can use the ratio method. For points passing through the origin A (0, 0), if the ratio of the y-coordinate to the x-coordinate for all other points is equal, they lie on the same straight line. For the point M (–3, –4), the ratio is 4/3 and for the point G (6, 8), the ratio is also 4/3. Thus, M, A and G are collinear.
For Detailed Solutions:
Visit NCERT Solutions for Class 9 Ganita Manjari Chapter 1 Orienting Yourself: The Use of Coordinates Question Answer:
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-1/
See lessUse your method (from Problem 6) to check if the points R (– 5, – 1), B (– 2, – 5) and C (4, – 12) are on the same straight line. Now plot both sets of points and check your answers.
Using the slope method, we calculate the steepness between pairs of points. The slope of segment RB is calculated as –4/3, which is approximately –1.33. The slope of segment BC is calculated as –7/6, which is approximately –1.16. Since these two slopes are not identical, the direction of the line chRead more
Using the slope method, we calculate the steepness between pairs of points. The slope of segment RB is calculated as –4/3, which is approximately –1.33. The slope of segment BC is calculated as –7/6, which is approximately –1.16. Since these two slopes are not identical, the direction of the line changes at point B. Therefore, the points R (–5, –1), B (–2, –5) and C (4, –12) do not lie on a straight line.
For Detailed Solutions:
Visit NCERT Solutions for Class 9 Ganita Manjari Chapter 1 Orienting Yourself: The Use of Coordinates Question Answer:
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-1/
See less