Find the coordinates of point \(P\) which divides the straight line \(AB\) in the ratio \(AP:PB\).
\(\begin{aligned} &A(5,1),B(-1,10);\\\\&AP:PB=2:1 \end{aligned}\)
\((2,7)\)
\((3,7)\)
For the following, point \(Q\) divides the straight line \(AB\) according to the ratio \(AQ:QB\).
Find the value of \(p\) and of \(q\).
\(\begin{aligned} &A(7,2q),Q(1,-2),B(q,p);\\\\&AQ:QB=3:2 \end{aligned}\)
\(\begin{aligned} p&=-\dfrac{2}{3}\\\\ q&=3\end{aligned}\)
\(\begin{aligned} p&=-\dfrac{2}{3}\\\\ q&=-3\end{aligned}\)
A straight line passes through \(A(5, 5)\) and \(B(–9, –2)\).
The point \(C\) divides the line segment \(AB\) such that
\(4AC = 3AB\).
Find the coordinates of \(C\).
\( \left(-\dfrac{11}{2},\dfrac{1}{4} \right)\)
\( \left(\dfrac{11}{2},\dfrac{1}{4} \right)\)
Point \(M(3, 6)\) divides a straight line joining point \(P(–5, 2)\) and point \(Q(5, 7)\) in the ratio of \(m : n\).
Find the ratio \(m : n\).
\(3 : 2\)
\(4 : 1\)
\(\begin{aligned} &A(10,p),Q(2p,-3),B(4,q);\\\\&AQ:QB=2:1 \end{aligned}\)
\(\begin{aligned} p&=-3\\\\ q&=6\end{aligned}\)
\(\begin{aligned} p&=-3\\\\ q&=-6\end{aligned}\)
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