Question 10 - End-of-Chapter Exercises - Chapter 1 Class 9 - Orienting Yourself: The Use of Coordinates (Ganita

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Question 10 Use 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). Formula for finding mid-point is Mid-point of (x1, y1) & (x2, y2) = ((𝒙_𝟏 + 𝒙_𝟐)/𝟐,(𝒚_𝟏+𝒚_𝟐)/𝟐) Given that M (–7, 1) is the midpoint of A (3, – 4) and B (x, y) So, we can write Coordinates of M = ((𝟑 + 𝒙)/𝟐,(−𝟒 + 𝒚)/𝟐) (–7, 1) = ((𝟑 + 𝒙)/𝟐,(−𝟒 + 𝒚)/𝟐) Comparing x and y coordinates Hence , x = –17 , y = 6 Thus, coordinates of point B are (-17, 6) −𝟕=(𝟑 + 𝒙)/𝟐 –7 × 2 = 3 + x –14 = 3 + x –14 – 3 = x – (14 + 3) = x –17 = x x = –17 𝟏 = (−4 + 𝑦)/2 1 × 2 = –4 + y 2 = –4 + y 2 + 4 = y 6 = y y = 6 Hence , x = –17 , y = 6 Thus, coordinates of point B are (-17, 6)