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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.
Given:
The line segment joining the points $A (-2, 2)$ and $B (2, 8)$ is divided into four equal parts.
To do:
We have to find the coordinates of the points which divide the line segment joining the points $A (-2, 2)$ and $B (2, 8)$ in four equal parts.
Solution:
Let $AB$ be a line segment whose ends points are $A (-2, 2)$ and $B (2, 8)$.
Let \( P, Q, R \) be the points which divide \( AB \) in four equal parts.
This implies,
\( A P=P Q=Q R=R B \)
\( Q \) is the mid-point of \( \mathrm{AB} \) and \( \mathrm{P} \) and \( \mathrm{R} \) are the mid points of \( A Q \) and \( Q B \) respectively.
Using mid-point formula, we get,
The coordinates of \( \mathrm{Q}= \left(\frac{-2+2}{2}, \frac{2+8}{2}\right) \)
\( =\left(\frac{0}{2}, \frac{10}{2}\right) \)
\( =(0,5) \)
The coordinates of \( \mathrm{P}= \left(\frac{-2+0}{2}, \frac{2+5}{2}\right) \)
\( =\left(\frac{-2}{2}, \frac{7}{2}\right) \)
\( =\left(-1, \frac{7}{2}\right) \)
\( =(-1,3.5) \)
The coordinates of \( \mathrm{R}= \left(\frac{0+2}{2}, \frac{5+8}{2}\right) \)
\( =\left(\frac{2}{2}, \frac{13}{2}\right) \)
\( =(1,6.5) \)
Therefore, the coordinates of the required points are \( \left(-1, 3.5\right), (0,5) \) and \( (1,6.5) \).
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