Determine the ratio in which the …
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Determine the ratio in which the line 2x+y-4=0 divdes the line segment joining the points A(2,-2) and B (3, 7)
Posted by _Jass_ Mahey_ 1 year ago
- 2 answers
Muhammad Amaan Rahman 𝔸𝕄𝔸𝔸ℕ 𝕄𝕌ℍ𝔸𝕄𝕄𝔸𝔻 1 year ago
in the ratio m₁: m₂ is given by the Section Formula.
P (x, y) = [(mx₂ + nx₁) / (m + n) , (my₂ + ny₁) / (m + n)]
Let the given line 2x + y - 4 = 0 divide the line segment joining the points A(2, - 2) and B(3, 7) in a ratio k: 1 at point C.
Coordinates of the point of divison
C (x, y) = [(3k + 2) / (k + 1), (7k - 2) / (k + 1)]
Hence, x = (3k + 2) / (k + 1), y = (7k - 2) / (k + 1)
This point C also lies on 2x + y - 4 = 0 .....(1)
By substituting the values of C(x, y) in Equation(1),
2[(3k + 2) / (k + 1)] + [(7k - 2) / (k + 1)] - 4 = 0
[6k + 4 + 7k - 2 - 4k - 4] / (k + 1) = 0 (By Cross multiplying & Transposing)
9k - 2 = 0
k = 2/9
Therefore, the ratio in which the line 2x + y - 4 = 0 divides the line segment joining the points A (2, 2) and B (3, 7) is 2:9 internally.
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_Jass_ Mahey_ 11 months, 3 weeks ago
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