What will be the value of y, if the ratio in which the point (\(\frac {3}{4}\), y) divides the line segment joining the points A(-1, 4) and B(6, 5)is 1:3?(a) y = \(\frac {9}{2}\)(b) y = \(\frac {5}{2}\)(c) y = \(\frac {9}{4}\)(d) y = \(\frac {5}{2}\)I got this question in an international level competition.My question is based upon Geometry in chapter Coordinate Geometry of Mathematics – Class 10

What will be the value of y, if the ratio in which the point (\(\frac

1.	What will be the value of y, if the ratio in which the point (\(\frac {3}{4}\), y) divides the line segment joining the points A(-1, 4) and B(6, 5)is 1:3?(a) y = \(\frac {9}{2}\)(b) y = \(\frac {5}{2}\)(c) y = \(\frac {9}{4}\)(d) y = \(\frac {5}{2}\)I got this question in an international level competition.My question is based upon Geometry in chapter Coordinate Geometry of Mathematics – Class 10
Answer» Right option is (a) y = \(\frac {9}{2}\) The explanation: Using, section formula x = \(\frac {mx_2+nx_1}{m+n}\) and y = \(\frac {my_2+ny_1}{m+n}\) The points are (-1, 4)and B(6, 5)in the ratio 1:3 ∴ x = \(\frac {1(6)+3(-1)}{1+3} = \frac {6-3}{4} = \frac {3}{4}\) y = \(\frac {1(6)+3(4)}{1+3} = \frac {6+12}{4} = \frac {18}{4}\) Therefore y = \(\frac {9}{2}\)

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