Share & grow the world's knowledge!
We want to connect the people who have knowledge to the people who need it, to bring together people with different perspectives so they can understand each other better, and to empower everyone to share their knowledge.
What 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 lessUse the connection you found to find the coordinates of B given that M (–7, 1) is the midpoint of A (3, – 4) and B (x, y).
The midpoint M (x, y) is the average of the coordinates of endpoints A and B. To find point B (x, y), we set up two simple equations: –7 = (3 + x) / 2 and 1 = (–4 + y) / 2. Solving for x, we multiply –7 by 2 to get –14, then subtract 3 to get –17. Solving for y, we multiply 1 by 2 to get 2, then addRead more
The midpoint M (x, y) is the average of the coordinates of endpoints A and B. To find point B (x, y), we set up two simple equations: –7 = (3 + x) / 2 and 1 = (–4 + y) / 2. Solving for x, we multiply –7 by 2 to get –14, then subtract 3 to get –17. Solving for y, we multiply 1 by 2 to get 2, then add 4 to get 6. Point B is (–17, 6).
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