Ramkrishnaneupane59idn
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Find the co-ordinates of the point of trisection of the line joining the points A(1,8) and B(4,2).


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Sagot :

Msm555idn

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 =[tex]\frac{1k}{2k}[/tex]= ratio 1:2

now

finding p

for this

[tex](m_1,m_2)=(1,2)[/tex]

For AB

[tex](x_1,y_1)=(1,8)[/tex]

[tex](x_2,y_2)=(4,2)[/tex]

now by using division formula

[tex](x,y)=(\frac{m_1x_2+m_2x_1}{m_1+m2},\frac{m_1y_2+m_2y_1}{m_1+m2})[/tex]

[tex]=(\frac{1*4+2*1}{1+2},\frac{1*2+2*8}{1+2})=(2,6)[/tex]

similarly

Q divides AB

Ratio of AQ and QB =[tex]\frac{2k}{1k}[/tex]= ratio 2:1

[tex](x_1,y_1)=(1,8)[/tex]

[tex](x_2,y_2)=(4,2)[/tex]

[tex](m_1,m_2)=(2,1)[/tex]

by using division formula

[tex](a,b)=(\frac{m_1x_2+m_2x_1}{m_1+m2},\frac{m_1y_2+m_2y_1}{m_1+m2})[/tex]

[tex]=(\frac{2*4+1*1}{2+1},\frac{2*2+1*8}{2+1})=(3,4)[/tex]

View image Msm555
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