What is the area of a triangle formed by the lines y=m_1 x+c_1,y=m_2 x+c_2 and y = 0?
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L1 : y = m1 x + c1 L2: m2 x + c2 = y
Conditions:
m1 and m2 are not same. Any of m1 and m2 is not zero.
X-axis intercept of L1 : x1 = - c1 / m1 L2: x2 = - c2 / m2
base = | x2 - x1 |
point of intersection of L1 and L2 - y coordinate gives height.
y = | (m1 c2 - m2 c1) / ( m1 - m2) | = altitude
Hence area = 1/2 (m1 c2-m2 c1)^2 / [ |m1 m2 (m1 - m2) | ]
Conditions:
m1 and m2 are not same. Any of m1 and m2 is not zero.
X-axis intercept of L1 : x1 = - c1 / m1 L2: x2 = - c2 / m2
base = | x2 - x1 |
point of intersection of L1 and L2 - y coordinate gives height.
y = | (m1 c2 - m2 c1) / ( m1 - m2) | = altitude
Hence area = 1/2 (m1 c2-m2 c1)^2 / [ |m1 m2 (m1 - m2) | ]
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