The area of the triangle formed by the lines x = 3, y = 4 and x = y is
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Answer:
x
2
−y
2
+2y=1
x
2
=(y−1)
2
Hence, the two lines are =
y=−x+1 and y=x+1
Equation of angle bisectors of these lines
x=0 and y=1
Intersection between the 3 lines is
A(0,3),B(0,1),C(2,1)
It can be seen that as the points A and B lie on y-axis only and BC is parallel to x-axis. Hence, △ABC is a right angled triangle.
Area=
2
1
×AB×BC
⟹
2
1
×2×2
⟹2
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