Find the mid point of the line formed by joining the points (1, 2) and

1.	Find the mid point of the line formed by joining the points (1, 2) and (3, 0) as there endpoints.1. (2, 1)2. (1, 1)3. (1, 2)4. (2, 2)
Answer» 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)

Find the mid point of the line formed by joining the points (1, 2) and (3, 0) as there endpoints.1. (2, 1)2. (1, 1)3. (1, 2)4. (2, 2)

Answer» 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)