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  • Find the coordinates of the points which divide the line segment joining A(– 2, 2) and B(2, 8) into four equal parts.

9.   Find the coordinates of the points which divide the line segment joining A (– 2, 2) and B(2, 8) into four equal parts.

Answers (1)

best_answer

From the figure:

lin eratio

Points C, D, and E divide the line segment AB into four equal parts.

Now, from the section formula, we can find the coordinates of Point C, D, and E.

Section Formula:

 P(x,y)= \left (\frac{m_{1}x_{2}+m_{2}x_{1}}{m_{1}+m_{2}} , \frac{m_{1}y_{2}+m_{2}y_{1}}{m_{1}+m_{2}} \right )

Here point D divides the line segment AB into two equal parts hence 

D(x_{2},y_{2})= \left (\frac{-2+2}{2} , \frac{2+8}{2} \right )

D(x_{2},y_{2})= \left (0 , 5 \right )

Now, point C divides the line segment AD into two equal parts hence

C(x_{1},y_{1})= \left (\frac{-2+0}{2} , \frac{2+5}{2} \right )

C(x_{2},y_{2})= \left (-1 , \frac{7}{2} \right )

Also, point E divides the line segment DB into two equal parts hence

E(x_{1},y_{1})= \left (\frac{2+0}{2} , \frac{8+5}{2} \right )

E(x_{2},y_{2})= \left (1 , \frac{13}{2} \right )

Posted by

Divya Prakash Singh

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