Correct Answer – Option 1 : (2, 1)

Concept:

If a point P divides a line joining points A(x1, y1) and B(x2, y2) in a ratio of m:n, then

\(\rm x_P ={nx_1 + mx_2\over n+m}\), \(\rm y_P ={ny_1 + my_2\over n+m}\) and \(\rm z_P ={nz_1 + mz_2\over n+m}\)

Calculation:

Given point are (1, 2) and (3, 0)

Midpoint divides the line in ratio 1 : 1

Let the mid-point be (x, y)

x = \(\rm {nx_1 + mx_2\over n+m}\)

⇒ x = \(\rm {1\times1 + 1\times3\over 1+1}\)

⇒ x = \(\rm {1 + 3\over 2}\) = 2

Similarly 

y = \(\rm {ny_1 + my_2\over n+m}\)

⇒ y = \(\rm {1\times2 + 1\times0\over 1+1}\)

⇒ y = \(\rm {2 + 0\over 2}\) = 1

∴ The mid-point is (2, 1)