Answer :
Given: equation passes through (1,2) and make an angle of 60° with the line x + y = 0
To find: equation of given line and the area of the triangle formed by the three lines
Explanation:
Let A(1, 2) be the vertex of the triangle ABC and x + y = 0 be the equation of BC.
Diagram:
Here, we have to find the equations of sides AB and AC, each of which makes an angle of 60∘ with the line x + y = 0.
We know the equations of two lines passing through a point x1,y1 and making an angle α with the line whose slope is m.
Here,
x1 = 1, y1 = 2, α = 60∘, m = - 1
So, the equations of the required sides are
and 
Solving x + y = 0 and 
, we get:
AB = BC = AD 
units
∴ Area of the required triangle 
square units
Hence, area of the required triangle 
square units
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