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 = $\frac {9}{2}$