# Find the equations of two straight lines passing through (1, 2) and making an angle of 600 with the lines x + y = 0. Find also the area of the triangle formed by the three lines.

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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