question_answer

Assertion [A]: Value of k for which area of the triangle with vertices (1, 1), (0, 2), (k, 0) is 3 sq. units are 4 and 8.

Reason [R]: Area of the triangle with vertices \[\left( {{x}_{1}},\,{{y}_{1}} \right),\,\left( {{x}_{2}},\,{{y}_{2}} \right)\left( {{x}_{3}},\,{{y}_{3}} \right)\]  is

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

B) Both A and R are individually true and R is not the correct explanation of A.

C) 'A' is true but 'R' is false

D) 'A' is false but 'R' is true

E) Both A and R are false.

Correct Answer: D

Solution :

Given: Area of triangle, \[\Rightarrow \,\,\left( 2-0 \right)-\left( 0-k \right)+\left( 0-2k \right)=\pm 6\] \[\Rightarrow \,\,\,2+k-2k=\pm 6\] \[\Rightarrow \,\,-k=\pm 6-2\] \[\Rightarrow \,\,\,-k=6-2;\,\,-k=-6-2\] \[\Rightarrow \,\,\,-k=4;\,\,-k=-8\] \[\Rightarrow \,\,\,k=-4;\,\,k=8\] \[\therefore \]Assertion [A] is false Also Reason (R) is true Hence option [D] is correct answer.