Just two lines
Line 1:- and
Line 2: - are two lines,
Area bounded by them are
: area between Y-axis, line 1 and line 2.
: area between X-axis, line 1 and line 2
: area between X-axis, Y-axis , line 1 and line 2
Which is always true?
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1 solution
x + y = a and x / m + y / t = 1 Their intersecting point is [ m ( m − t a − t ) , t ( t − m a − m ) ]
Now, by taking determinent we can get A1 and A2.
A1 : (0,t), (0,a) , [ m ( m − t a − t ) , t ( t − m a − m ) ]
A2 : (m,0) , (a,0) , [ m ( m − t a − t ) , t ( t − m a − m ) ]
by determinent,
A1 = 1 / 2 ∣ ( m / m − t ) ( a − t ) 2 |\
A2 = 1 / 2 ∣ ( t / m − t ) ( a − m ) 2
Now, A 1 / A 2 = ∣ ( m / t ) [ ( a − t ) / ( a − m ) ] 2 ∣
now, if m < t < a , ( a − m ) > ( a − t ) and m < t so A 1 / A 2 < 1
and for all other options it is not always true.