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  • Let P and Q be the points of trisection of the line segment joining the point A(2,-2) and B (-7,4) such that P is nearer to A. Find the coordinates of P and Q       </p

Let P and Q be the points of trisection of the line segment joining the point A(2,-2) and B (-7,4) such that P is nearer to A. Find the coordinates of P and Q 

 

 

 

 
 
 
 
 

Answers (1)

A = ( x_1 , y_1 ) = ( 2,-2) \\\\ B = ( x_2 , y_2 )= ( -7 , 4 )

According to question 

\frac{AP}{BP} = \frac{1}{2} \\\\ \frac{m}{n} = \frac{1}{2} ---- (1) \\\\ \frac{AQ }{BQ } = \frac{2}{1} \\\\\ \frac{m}{n} = \frac{2}{1} ----- ( 2) \\\\ coordinates \: \: of \: \: P = \left ( \frac{mx_2 + n x_1 }{m+n}, \frac{my_2 + n y_1}{m+n} \right )\\\\\\ \left ( \frac{1 \times (-7)+ 2 \times 2}{1 + 2 }, \frac{2 \times 4 + 2 \times (-2)}{1+2 } \right ) \\\\ = \left ( \frac{-7+4}{3}, \frac{4-4}{3} \right )\\\\

\left ( \frac{-3}{3}, \frac{0}{3}\right ) \\\\ P = (-1,0)

Coordinates of Q =

= \left ( \frac{mx_2 + n x_1 }{m+n}, \frac{my_2 + n y_1}{m+n} \right )\\\\\\ \left ( \frac{2 \times (-7)+ 1\times 2}{ 2+1 }, \frac{2 \times 4 + 1\times (-2)}{2+1 } \right ) \\\\ = \left ( \frac{-14+2}{3}, \frac{8-2}{3} \right )\\\\ = \left ( \frac{-12}{3}, \frac{6}{3} \right )\\\\ Q = ( -4,2)

Posted by

Ravindra Pindel

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