questionr
Early access
Exams
Joint Entrance Examination
Mathematics
Matrices and Determinants
Question 395
Question 395 of 472
Medium
MCQ
Let A(a, 0), B(b, 2b + 1) and C(0, b), b \[\ne\] 0, |b| \[\ne\] 1, be points such that the area of triangle ABC is 1 sq. unit, then the sum of all possible values of a is :
A
\[{{ - 2b} \over {b + 1}}\]
B
\[{{2b} \over {b + 1}}\]
C
\[{{2{b^2}} \over {b + 1}}\]
D
\[{{ - 2{b^2}} \over {b + 1}}\]
Check answer
Press A-D to select · Enter to check
Solutions · 1
Post your solution
Official solution
\[\left| {{1 \over 2}\left| {
(
a
0
1
b
2
b
+
1
1
0
b
1
)
\begin{pmatrix} a & 0 & 1 \\ b & {2b + 1} & 1 \\ 0 & b & 1 \\ \end{pmatrix}
a
b
0
0
2
b
+
1
b
1
1
1
} \right|} \right| = 1\] \[ \Rightarrow \left| {
(
a
0
1
b
2
b
+
1
1
0
b
1
)
\begin{pmatrix} a & 0 & 1 \\ b & {2b + 1} & 1 \\ 0 & b & 1 \\ \end{pmatrix}
a
b
0
0
2
b
+
1
b
1
1
1
} \right| = \pm \,2\] \[ \Rightarrow a(2b + 1 - b) - 0 + 1({b^2} - 0) = \pm \,2\] \[ \Rightarrow a = {{ \pm \,2 - {b^2}} \over {b + 1}}\] \[\therefore\] \[a = {{2 - {b^2}} \over {b + 1}}\] and \[a = {{ - 2 - {b^2}} \over {b + 1}}\] Sum of possible values of 'a' is \[ = {{ - 2{b^2}} \over {a + 1}}\]
Answer the question to unlock
Previous
Next