Question

What will be the coordinates of B, if the point C\((\frac {29}{7}, \frac {46}{7} )\), divides the line segment joining A (5, 8) and B (a, b) in the ratio 2:5?

(a) a = 2, b = 3

(b) a = -2, b = 3

(c) a = 2, b = -3

(d) a = -2, b = -3

I got this question during an online interview.

The above asked question is from Geometry in portion Coordinate Geometry of Mathematics – Class 10

Answer 1

Correct answer is (a) a = 2, b = 3

To explain I would say: Using, section formula x = \(\frac {mx_2+nx_1}{m+n}\) and y = \(\frac {my_2+ny_1}{m+n}\)

The points are A(5, 8)and B(a, b)in the ratio 2:5

∴ x = \(\frac {2(a)+5(5)}{2+5} = \frac {2a+25}{7}\)

y = \(\frac {2(b)+5(8)}{2+5} = \frac {2b+40}{7}\)

But the coordinates of C are \((\frac {29}{7}, \frac {46}{7} )\)

Therefore, \(\frac {2a+25}{7} = \frac {29}{7}\)

a = 2

\(\frac {2b+40}{7} = \frac {46}{7}\)

b = 3