question_answer

Assertion (A): The coordinates of the points which divide the line segment joining \[A(2,-8)\] and \[B(-3,-7)\] into three equal parts are \[\left( \frac{1}{3},-\frac{23}{3} \right)\]and \[\left( -\frac{4}{3},-\frac{22}{3} \right)\].

Reason (R): The points which divide AB in the ratio \[1:3\]and \[3:1\]are called points of trisection of AB.

A) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A)

B) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).

C) Assertion (A) is true but reason (R) is false.

D) Assertion (A) is false but reason (R) is true.

Correct Answer: C

Solution :

[c] Let P and Q be the points which divide \[A(2,-8)\]and \[B(-3,-7)\]into three equal parts.

\[\therefore \,\,\,\,\,\,\,\,\,\,\,AP:PB=1:2\]

So, coordinates of

\[P=\left( \frac{-3+4}{3},\frac{-7-16}{3} \right)\,\,=\,\,\left( \frac{1}{3},-\frac{23}{3} \right)\]

Also,      \[AQ:QB=2:1\]

\[\therefore \] Coordinates of

\[Q=\left( \frac{-6+2}{3},\frac{-14-8}{3} \right)\,\,=\left( -\frac{4}{3},-\frac{-22}{3} \right)\]

\[\therefore \] Assertion [a] is true but reason (R) is false.