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]
