Question

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 1

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 = \(\frac {9}{2}\)