Question

The area of triangle formed by lines y=0, y-x= 2and 3x +2y=6 is
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Answer 1

Step-by-step explanation:

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Find the area of the triangle formed by the lines y−x=0,x+y=0 and x−k=0

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Solution

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The equation of the given lines are

y−x=0....(1)

x+y=...(2)

x−k=0...(3)

The point of intersection of lines (1) and (2) is given by

x=0 and y=0

The point of intersection of lines (2) and (3) is given by

x=k and y=−k

The point of intersection of lines(3) and (1) is given by

x=k and y=k

Thus, the vertices of the triangle formed by the three given lines are (0,0),(k,−k), and (k,k)

We know that the area of the triangle whose vertices are (x

1

,y

1

),(x

2

,y

2

), and (x

3

,y

3

) is

2

1

∣x

1

(y

2

−y

3

)+x

2

(y

3

−y

1

)+x

3

(y

1

−y

2

)∣

Therefore, area of the triangle formed by the three given lines,

=

2

1

∣0(−k−k)+k(k−0)+k(0+k)∣square unts

=

2

1

∣

∣

∣

k

2

+k

2

∣

∣

∣

square units

=

2

1

∣

∣

∣

2k

2

∣

∣

∣

=k

2

square