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Find the area of the triangle formed by the lines x = 0, y = 1 and 2x + y = 2.

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The given equations are

x = 0 …(i)

y = 1 …(ii)

and 2x + y = 2 …(iii)

Let eq. (i), (ii) and (iii) represents the sides AB, BC and AC respectively of ΔABC

From eq. (i) and (ii), we get x = 0 and y = 1

Thus, AB and BC intersect at (0, 1)

Solving eq. (ii) and (iii), we get

y = 1 …(ii)

and 2x + y = 2 …(iii)

Putting the value of y = 1 in eq. (iii), we get

2x + 1 = 2

⇒ 2x = 1

⇒ x = 1/2

Thus, BC and AC intersect at (1/2, 1)

Now, Solving eq. (iii) and (i), we get

2x + y = 2 …(iii)

and x = 0 …(i)

Putting the value of x = 0 in eq. (iii), we get

y = 2

Thus, AC and AB intersect at (0, 2)

So, vertices of triangle ABC are: (0, 1), (1/2, 1) and (0, 2)

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