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Find the Co-ordinate of a triangle formed by x + y = 2 and co-ordinate axis. (a) (0, 0) (0, 2) (2, 0) (b) (3, 0) (0, 3) (0, 0) (c) 10.0) (0, -2), (-2, 0) (d) (0, 2) (0.-2) (2, 0)​

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Answer:

Answer:

The co-ordinate axes has its origin at O(0,0) and triangle is formed by the line 3x+4y=12

The line 3x+4y=12 cuts the x−axis at y=0 ∴ co-ordinate of x−axis is (4,0) by substituting y=0 in 3x+4y=12 then 3x=12 or x=4

The line 3x+4y=12 cuts the y−axis at x=0 ∴ co-ordinate of y−axis is (0,3) by substituting y=0 in 3x+4y=12 then 4y=12 or y=3

Now the distance OA=4units and that of OB=3units

Using formula for incentre of a triangle we have

I(x,y)=(

3

ax

1

+bx

2

+cx

3

,

3

ay

1

+by

2

+cy

3

)

Since △BOA is a right angled triangle

Using Pythagoras theorem, AB

2

=OA

2

+OB

2

=4

2

+3

2

=16+9=25

or AB=5 sq.units

∴ b=4,a=3,c=5

I(x,y)=(

3+4+5

3×4+0+0

,

3+4+5

0+4×3+0

)=(

12

12

,

12

12

)=(1,1)

210
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