Question

Assertion (A): The coordinates of a point which divides a line segment joining the points (–3, 4) and (7, –6) in the ratio 1 : 2 internally are \(\left(\frac{1}{3}, \frac{2}{3}\right)\).

Reason (R): The coordinates of the point which divides the line segment. joining the points \(\left(x_{1}, y_{1}\right)\) and \(\left(x_{2}, y_{2}\right)\) internally in the ratio \(m : n\) are given by \(\left(\frac{mx_{2} + nx_{1}}{m + n}, \frac{my_{2} + ny_{1}}{m + n}\right)\)

Options

• Both A and R are true, and R is the correct explanation of A.

• Both A and R are true, but R is not the correct explanation of A.

• A is true, but R is false.

• A is false, but R is true.

Answer 1

Both A and R are true, and R is the correct explanation of A.

Explanation:

For A(–3, 4), B(7, –6), m = 1, n = 2: 

$$x = \frac{1(-7) + 2(-3)}{1 + 2} = \frac13$$

$$y = \frac{1(-6) + 2(4)}{3} = \frac23$$

Thus Assertion is true; Reason gives the standard internal-section formula and correctly explains it.