Question

Find the coordinates of the points of trisection of the lines joining the points A(-3,0)
and B(6,6). Also find AP.

Answer 1

Step-by-step explanation:

A(−3,0) B(6,6)

Let A(−3,0) be the first point and B(6,6) be the second point and P and Q be the internally trisecting point

Let AB=PQ=QB=K

PB=PQ+OB=2K

And AQ=AP+PQ=2K

AP=PB=1:2

And AQ:QB=2:1

P divides a,b internally in ratio 1:2 while Q divides internally in the ratio 2:1 does coordinates of p and q are

P(

1+2

1(6)+2×(−3)

,

1+2

1(6)+2(0)

)=P(0,2)

Q(

1+2

2(6)+1×(−3)

,

1+2

2(6)+1(0)

)=Q(

3

9

,

3

12

)=Q(3,4)

P(0,2) and Q(3,4) are point of trisection

Answer 2

A(−3,0) B(6,6)

Let A(−3,0) be the first point and B(6,6) be the second point and P and Q be the internally trisecting point

Let AB=PQ=QB=K

PB=PQ+OB=2K

And AQ=AP+PQ=2K

AP=PB=1:2

And AQ:QB=2:1

P divides a,b internally in ratio 1:2 while Q divides internally in the ratio 2:1 does coordinates of p and q are

P( 1+21(6)+2×(−3) ,1+21(6)+2(0) )=P(0,2)

Q( 1+22(6)+1×(−3) ,1+22(6)+1(0) )=Q( 39,312 )=Q(3,4)

P(0,2) and Q(3,4)

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