question_answer

Directions: Each of these questions contains two statements: Assertion [A] and Reason [R]. Each of these questions also has four alternative choices, any one of which is the correct answer. You have to select one of the codes [a], [b], [c] and [d] given below.

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

Reason The points which divide AB in the ratio 1 : 3 and 3 : 1 are called points to trisection of AB.

 

A) A is true, R is true; R is a correct explanation for A.

B) A is true, R is true; R is not a correct explanation for A.

C) A is true; R is False.

D) A is false; R is true.

Correct Answer: C

Solution :

\[AP:PB=1:2\]

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

\[=\left( \frac{-4}{3},\frac{-22}{3} \right)\]

Hence, Assertion is true but Reason is false