Using vertex properties: A = E + F – D, giving (1, 7). B = D + F – E, giving (–1, –1). C = D + E – F, giving (11, 3). These coordinates form the original triangle ABC.
The 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.
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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/