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  • If the line segment joining the points A(2, 1) and B(5, –8) is trisected at the points P and Q, find the coordinates of P.      

If the line segment joining the points A(2, 1) and B(5, –8) is trisected at the points P and Q, find the coordinates of P.

 

 

 
 
 
 
 

Answers (1)

Given :

AP=PQ=QB\;\;\;\;\;\;-(1)

A=(x_1,y_1)=(2,1)

B=(x_2,y_2)=(5, - 8)

Let P=(x,y)

\frac{AP}{PB}=\frac{AP}{PQ+QB}=\frac{AP}{AP+AP}=\frac{1}{2}   (From (i))

\Rightarrow \frac{AP}{PB}=\frac{1}{2}

Applying section formula :

P(x,y)=\left ( \frac{mx_2 + nx_1}{m+n}, \frac{my_2+ny_1}{m+n} \right )

                =\left ( \frac{1\times 5 + 2\times 2}{1+2}, \frac{1\times (-8)+2\times 1}{1+2} \right )

=\left ( \frac{5 + 4}{3}, \frac{-8+2}{3} \right )

P(x,y)=\left ( 3,-2 \right )

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Safeer PP

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