a-maths~~~~~

a)
x-2y+2=0.........(1)
2x-y-2=0.........(2)

x-2(2x-2)+2=0
x=2

put x=2 into (2),
2(2)-y-2=0
y=2

A=(2,2)


b)
since the line passes through (0,0)
eqt of L : y=mx


c)
put y=mx into (1)
x-2(mx)+2=0
x-2mx+2=0
x=2/(2m-1)

when x=2/(2m-1), y=2m/(2m-1)


put y=mx into (2)
2x-mx-2=0
x=2/(2-m)

when x=2/(2-m), y=2m/(2-m)

vertex of triangle:
A(2,2)
B(2/(2m-1), 2m/(2m-1))
C(2/(2-m), 2m/(2-m))

Area
= | 2 2 |
1/2 |2/(2m-1), 2m/(2m-1) |
|2/(2-m), 2m/(2-m) |
| 2 2 |
=1/2 |4m/(2m-1)+2m/(2m-1)(2-m)+4/(2-m)-4/(2m-1)-4m/(2m-1)(2-m)-4m/(2-m)|
=1/2 |4m/(2m-1)+4m/(2m-1)(2-m)+4/(2-m)-4/(2m-1)-4m/(2m-1)(2-m)-4m/(2-m)|

=1/2 |4m/(2m-1) -4/(2m-1) +4/(2-m) -4m/(2-m) |
=1/2 |4 (m-1)/(2m-1) + 4(1-m)/(2-m)|
=1/2 |4 (m-1)/(2m-1) - 4(m-1)/(2-m)|
=2 |(m-1)/(2m-1) - (m-1)(2-m)|
=2 |(m-1) [1/(2m-1)-1/(2-m)]|
=2 |(m-1) [(-3m+3)/(2m-1)(2-m)]|
=2 |3(m-1) (m-1) [-1/(2m-1)(2-m)] |
=6(m-1)2 |1/(2m-1)(2-m) |