Question

3) Find the co-ordinates of the points which divides the line segment A(-4,4) and
(3,7) into four equal parts.​

Answer 1

$\textbf{Given:}$

$A(-4,4)\;\text{and}\;B(3,7)$

$\textbf{To find:}$

$\text{The co-ordinates of the points which divides AB into four equal parts}$

$\textbf{Solution:}$

$\text{Let P be the midpoint of AB}$

$\text{Then, P is}\;(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

$\implies\;P\,(\frac{-4+3}{2},\frac{4+7}{2})$

$\implies\bf\;P\,(\frac{-1}{2},\frac{11}{2})$

$\text{Let Q be the midpoint of AP}$

$\text{Then, Q is}\;(\frac{-4+\frac{(-1)}{2}}{2},\frac{4+\frac{11}{2}}{2})$

$\implies\,Q\,(\frac{\frac{-9}{2}}{2},\frac{\frac{19}{2}}{2})$

$\implies\bf\,Q\,(\frac{-9}{4},\frac{19}{4})$

$\text{Let R be the midpoint of BP}$

$\text{Then, R is}\;(\frac{3+\frac{(-1)}{2}}{2},\frac{7+\frac{11}{2}}{2})$

$\implies\,R\,(\frac{\frac{5}{2}}{2},\frac{\frac{25}{2}}{2})$

$\implies\bf\,R\,(\frac{5}{4},\frac{25}{4})$

$\therefore\textbf{The points which divide AB into four equal parts are}$

$\bf(\frac{-1}{2},\frac{11}{2}),\,(\frac{-9}{4},\frac{19}{4}),\textbf{and}\,\bf(\frac{5}{4},\frac{25}{4})$

Find more:

The line segment joining the points (3,-1) and (-6,5) is trisected. find the coordinate of the point of trisection.

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