This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Here's how to solve question 6: Given points are P(11, 1) and Q(2, 7). Let P = (x_1, y_1) = (11, 1) and Q = (x_2, y_2) = (2, 7). The section formula for a point (x, y) that divides the line segment joining (x_1, y_1) and (x_2, y_2) in the ratio m:n is: For internal division: (x, y) = ( (nx_1 + mx_2)/(m+n), (ny_1 + my_2)/(m+n) ) For external division: (x, y) = ( (nx_1 - mx_2)/(n-m), (ny_1 - my_2)/(n-m) ) i) Internally in the ratio 2:1 Here, m=2 and n=1. Step 1: Apply the internal division formula for the x-coordinate. x = (1 · (11) + 2 · (2))/(2+1) = (11 + 4)/(3) = (15)/(3) = 5 Step 2: Apply the internal division formula for the y-coordinate. y = (1 · (1) + 2 · (7))/(2+1) = (1 + 14)/(3) = (15)/(3) = 5 The coordinates of the point dividing PQ internally in the ratio 2:1 are (5, 5). ii) Externally in the ratio 3:5 Here, m=3 and n=5. Step 3: Apply the external division formula for the x-coordinate. x = (5 · (11) - 3 · (2))/(5-3) = (55 - 6)/(2) = (49)/(2) Step 4: Apply the external division formula for the y-coordinate. y = (5 · (1) - 3 · (7))/(5-3) = (5 - 21)/(2) = (-16)/(2) = -8 The coordinates of the point dividing PQ externally in the ratio 3:5 are ((49)/(2), -8). Send me the next one 📸