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.
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Visit NCERT Solutions for Class 9 Ganita Manjari Chapter 1 Orienting Yourself: The Use of Coordinates Question Answer:
(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.
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Visit NCERT Solutions for Class 9 Ganita Manjari Chapter 1 Orienting Yourself: The Use of Coordinates Question Answer:
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:
Trisection means dividing a segment into three equal lengths. First, find the total distance: x increases by 12 (16 minus 4) and y decreases by 9 (–2 minus 7). Dividing these by three gives steps of 4 for x and –3 for y. Starting from A (4, 7) and adding one step gives P (8, 4). Adding another stepRead more
Trisection means dividing a segment into three equal lengths. First, find the total distance: x increases by 12 (16 minus 4) and y decreases by 9 (–2 minus 7). Dividing these by three gives steps of 4 for x and –3 for y. Starting from A (4, 7) and adding one step gives P (8, 4). Adding another step to P gives Q (12, 1). These two points, P and Q, trisect the segment AB.
For Detailed Solutions:
Visit NCERT Solutions for Class 9 Ganita Manjari Chapter 1 Orienting Yourself: The Use of Coordinates Question Answer:
(i) By calculating the distance from the origin O (0, 0) to points A, B and C using the formula (x squared plus y squared), we find all equal 65. Thus, they lie on circle K with a radius of the square root of 65. (ii) For point D (–5, 6), the sum is 61, which is less than 65, placing it inside the cRead more
(i) By calculating the distance from the origin O (0, 0) to points A, B and C using the formula (x squared plus y squared), we find all equal 65. Thus, they lie on circle K with a radius of the square root of 65. (ii) For point D (–5, 6), the sum is 61, which is less than 65, placing it inside the circle. For point E (0, 9), the sum is 81, placing it outside the circle.
For Detailed Solutions:
Visit NCERT Solutions for Class 9 Ganita Manjari Chapter 1 Orienting Yourself: The Use of Coordinates Question Answer:
Use 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 lessLet P, Q be points of trisection of AB, with P closer to A and Q closer to B. Using your knowledge of how to find the coordinates of the midpoint of a segment, how would you find the coordinates of P and Q? Do this for the case when the points are A (4, 7) and B (16, –2).
Trisection means dividing a segment into three equal lengths. First, find the total distance: x increases by 12 (16 minus 4) and y decreases by 9 (–2 minus 7). Dividing these by three gives steps of 4 for x and –3 for y. Starting from A (4, 7) and adding one step gives P (8, 4). Adding another stepRead more
Trisection means dividing a segment into three equal lengths. First, find the total distance: x increases by 12 (16 minus 4) and y decreases by 9 (–2 minus 7). Dividing these by three gives steps of 4 for x and –3 for y. Starting from A (4, 7) and adding one step gives P (8, 4). Adding another step to P gives Q (12, 1). These two points, P and Q, trisect the segment AB.
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(i) Given the points A (1, – 8), B (– 4, 7) and C (–7, – 4), show that they lie on a circle K whose center is the origin O (0, 0). What is the radius of circle K? (ii) Given the points D (–5, 6) and E (0, 9), check whether D and E lie within the circle, on the circle or outside the circle K.
(i) By calculating the distance from the origin O (0, 0) to points A, B and C using the formula (x squared plus y squared), we find all equal 65. Thus, they lie on circle K with a radius of the square root of 65. (ii) For point D (–5, 6), the sum is 61, which is less than 65, placing it inside the cRead more
(i) By calculating the distance from the origin O (0, 0) to points A, B and C using the formula (x squared plus y squared), we find all equal 65. Thus, they lie on circle K with a radius of the square root of 65. (ii) For point D (–5, 6), the sum is 61, which is less than 65, placing it inside the circle. For point E (0, 9), the sum is 81, placing it outside the circle.
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