What are the coordinates of the point which divides the line joining (-1, 7) and (4, 3) in the ratio 2:3?
Let the coordinates of the point be P(x, y) which divides the line segment joining the points (-1, 7) and (4, - 3) in the ratio 2 : 3 Let two points be A (x₁, y₁) and B(x₂, y₂). P (x, y) divides internally the line joining A and B in the ratio m₁: m₂. Then, coordinates of P(x, y) is given by the section formula P (x, y) = [(mx₂ + nx₁ / m + n), (my₂ + ny₁ / m + n)] Let x₁ = - 1, y₁ = 7, x₂ = 4 and y₂ = - 3, m = 2, n = 3 By Section formula, P (x, y) = [(mx₂ + nx₁ / m + n) , (my₂ + ny₁ / m + n)] --- (1) By substituting the values in the equation (1) x = [2 × 4 + 3 × (- 1)] / (2 + 3) and y = [2 × (- 3) + 3 × 7] / (2 + 3) x = (8 - 3) / 5 and y = (- 6 + 21) / 5 x = 5/5 = 1 and y = 15/5 = 3 Therefore, the coordinates of point P are (1, 3).
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