In what ratio is the line segment joining the points A(2, 4) and B(6, 5) divided by the y-axis?(a) 2:1 (internally)(b) 2:1 (externally)(c) 3:1 (internally)(d) 3:1 (externally)This question was addressed to me in quiz.I want to ask this question from Geometry in portion Coordinate Geometry of Mathematics – Class 10

In what ratio is the line segment joining the points A(2, 4) and B(6,

1.	In what ratio is the line segment joining the points A(2, 4) and B(6, 5) divided by the y-axis?(a) 2:1 (internally)(b) 2:1 (externally)(c) 3:1 (internally)(d) 3:1 (externally)This question was addressed to me in quiz.I want to ask this question from Geometry in portion Coordinate Geometry of Mathematics – Class 10
Answer» The CORRECT answer is (d) 3:1 (externally) Explanation: Let the ratio in which the y-axis divides the line segment joining the points A(2, 4) and B(6, 5) be K:1 Using, section formula x = \(\frac {mx_2+nx_1}{m+n}\) and y = \(\frac {my_2+ny_1}{m+n}\) The points are A(2, 4) and B(6, 5) and the ratio is k:1 ∴ x = \(\frac {k(6)+1(2)}{k+1} = \frac {6K+2}{k+1}\) y = \(\frac {k(5)+1(4)}{k+1} = \frac {5k+4}{k+1}\) Since, the point is on y-axis. Hence, the x-coordinate will be zero. ∴ 0 = \(\frac {6k+2}{k+1}\) 0 = 6k + 2 k = \(\frac {-6}{2}\) = -3 The ratio in which the y-axis CUTS the line segment joining the points A(2, 4) and B(6, 5) will be 3:1 (externally).

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