P is one-third and Q is two-thirds along the segment. The total change in x is 12 and y is –9. Applying these shifts to A gives P (8, 4) and Q (12, 1).
Let 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).
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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/