Find the coordinates of the point which divides the join of (-1, 7) and (4, - 3) in the ratio 2 : 3
Solution:
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).
☛ Check: NCERT Solutions Class 10 Maths Chapter 7
Video Solution:
Find the coordinates of the point which divides the join of (-1, 7) and (4, - 3) in the ratio 2 : 3
NCERT Class 10 Maths Solutions Chapter 7 Exercise 7.2 Question 1
Summary:
The coordinates of the point which divides the join of (- 1, 7) and (4, - 3) in the ratio 2 : 3 is (1, 3).
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