Question

If the line 3x+4y-24=0 intersects the x-axis at the point A and the y-axis at the point B, then the incentre of the triangle OAB, where O is the origin, is​

Answer 1

Answer:

Answer

Line intersects the x-axis at x=8,y=0

⇒A=(8,0)

Line intersects the y-axis at x=0,y=6

⇒B=(0,6)

Incenter of triangle OAB =(

a+b+c

ax

1

+bx

2

+cx

3

),(

a+b+c

ay

1

+by

2

+cy

3

)

Where O=(x

1

,y

1

)=(0,0),A=(x

2

,y

2

)=(8,0),B=(x

3

,y

3

)=(0,6)

⇒AB=10,OB=6,OA=8

⇒Incenter =(

10+8+6

10.0+6.8+8.0

,

10+8+6

10.0+6.0+8.6

)

⇒incenter =(2,2)