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Question

Find the area of the triangle formed by the lines y=m1x+c1,y=m2x+c2 and x = 0

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Solution

Let the sides AC, AB and BC of ABC be represented by the equations:

m1xy+c1=0.....(i)

m2xy+c2=0.....(ii)

x=0.....(iii)

On solving (i) and (ii) by cross multiplication, we have,

x(C2+C1)=y(m2c1m1c2)=1(m1+m2)

x=(c1c2)(m2m1) and y=(m2c1m1c2)(m2m1)

Thus, the lines AC and AB intersect at A (c1c2m2m1,m2c1m1c2m2m1)

On solving (ii) and (iii), we get B(0,c2).

On solving (i) and (ii), we get C(0,c1)

area of ABC is given by,

A =12(c1c2)(m2m1).(c2c1)+0+0

=12(c1c2)2|m1m2|


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