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Consider 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 lessUsing the origin as one vertex, plot the vertices of: (i) A right-angled isosceles triangle. (ii) An isosceles triangle with one vertex in Quadrant III and the other in Quadrant IV.
(i) To form a right-angled isosceles triangle, use origin O (0, 0) as the vertex. Place A at (5, 0) and B at (0, 5) to create equal sides of 5 units along the axes. (ii) For the second triangle, use O (0, 0) as the top vertex. Place P at (–3, –4) in Quadrant III and Q at (3, –4) in Quadrant IV. BothRead more
(i) To form a right-angled isosceles triangle, use origin O (0, 0) as the vertex. Place A at (5, 0) and B at (0, 5) to create equal sides of 5 units along the axes. (ii) For the second triangle, use O (0, 0) as the top vertex. Place P at (–3, –4) in Quadrant III and Q at (3, –4) in Quadrant IV. Both P and Q are 5 units from the origin, ensuring the triangle is isosceles.
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