Question

Find the co-ordinates of the point of trisection of the line joining the points A(1,8) and B(4,2).

please answer as quickly as possible with correct answer .
Don't answer randomly ​

Answer 1

coordinates of the point are (2,6) and (3,4)

Answer:

Solution given:

let the given point be A(1,8) and B(4,2).

P and Q are the two points on AB such that

AP=PQ=QB=k

now

comparing AP and PB

AP=k

PB=2k

ratio of AP and PB =
`(1k)/(2k)`= ratio 1:2

now

finding p

for this

`(m_1,m_2)=(1,2)`

For AB

`(x_1,y_1)=(1,8)`

`(x_2,y_2)=(4,2)`

now by using division formula

`(x,y)=((m_1x_2+m_2x_1)/(m_1+m2),(m_1y_2+m_2y_1)/(m_1+m2))`

`=((1*4+2*1)/(1+2),(1*2+2*8)/(1+2))=(2,6)`

similarly

Q divides AB

Ratio of AQ and QB =
`(2k)/(1k)`= ratio 2:1

`(x_1,y_1)=(1,8)`

`(x_2,y_2)=(4,2)`

`(m_1,m_2)=(2,1)`

by using division formula

`(a,b)=((m_1x_2+m_2x_1)/(m_1+m2),(m_1y_2+m_2y_1)/(m_1+m2))`

`=((2*4+1*1)/(2+1),(2*2+1*8)/(2+1))=(3,4)`