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Using 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 lessThe midpoints of the sides of triangle ABC are the points D, E and F. Given that the coordinates of D, E and F are (5, 1), (6, 5) and (0, 3), respectively, find the coordinates of A, B and C.
In a triangle, any vertex can be found by adding the two adjacent midpoints and subtracting the opposite midpoint. To find vertex A (opposite D), we calculate A = E + F – D, resulting in (1, 7). To find vertex B (opposite E), we calculate B = D + F – E, resulting in (–1, –1). To find vertex C (opposRead more
In a triangle, any vertex can be found by adding the two adjacent midpoints and subtracting the opposite midpoint. To find vertex A (opposite D), we calculate A = E + F – D, resulting in (1, 7). To find vertex B (opposite E), we calculate B = D + F – E, resulting in (–1, –1). To find vertex C (opposite F), we calculate C = D + E – F, resulting in (11, 3). These are the three vertices.
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