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Directions: Questions number $19$ and $20$ are Assertion and Reason based questions carrying $1$ mark each. Two statements are given, one labelled as Assertion (A) and the other is labelled as Reason (R). Select the correct answer to these questions from the codes (A), (B), (C) and (D) as given below:
(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
(B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
(C) Assertion (A) is true, but Reason (R) is false.
(D) Assertion (A) is false, but Reason (R) is true.
Assertion (A): The point which divides the line segment joining the points A $(1, 2)$ and B$(-1, 1)$ internally in the ratio $1: 2$ is $(\frac{-1}{3}, \frac{5}{3})$
Reason (R): The coordinates of the point which divides the line segment joining the points A $(x_1, y_1)$ and B$(x_2, y_2)$ in the ratio $m_1: m_2$ are $(\frac{m_1x_2 + m_2x_1}{m_1 + m_2}, \frac{m_1y_2 + m_2y_1}{m_1 + m_2})$
(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
(B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
(C) Assertion (A) is true, but Reason (R) is false.
(D) Assertion (A) is false, but Reason (R) is true.
Assertion (A): The point which divides the line segment joining the points A $(1, 2)$ and B$(-1, 1)$ internally in the ratio $1: 2$ is $(\frac{-1}{3}, \frac{5}{3})$
Reason (R): The coordinates of the point which divides the line segment joining the points A $(x_1, y_1)$ and B$(x_2, y_2)$ in the ratio $m_1: m_2$ are $(\frac{m_1x_2 + m_2x_1}{m_1 + m_2}, \frac{m_1y_2 + m_2y_1}{m_1 + m_2})$
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Sol.
(D) Assertion (A) is false, but Reason(R) is true.
(D) Assertion (A) is false, but Reason(R) is true.