Find the coordinates of the points which divide the line segment joining the points $(-4, 0)$ and $(0, 6)$ in four equal parts.

Given:

The line segment joining the points $(-4, 0)$ and $(0, 6)$ 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 $(-4, 0)$ and $(0, 6)$ in four equal parts.

Solution:

Let $AB$ be a line segment whose ends points are $A (-4, 0)$ and $B (0, 6)$.

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 \( \mathrm{Q}= \left(\frac{-4+\dot{0}}{2}, \frac{0+6}{2}\right) \)

\( =\left(\frac{-4}{2}, \frac{6}{2}\right) \) 

\( =(-2,3) \)

The coordinates of \( \mathrm{P}= \left(\frac{-4-2}{2}, \frac{0+3}{2}\right) \)

\( =\left(\frac{-6}{2}, \frac{3}{2}\right) \)

\( =\left(-3, \frac{3}{2}\right) \)

\( =(-3,1.5) \) 

The coordinates of \( \mathrm{R}= \left(\frac{-2+0}{2}, \frac{3+6}{2}\right) \)

\( =\left(\frac{-2}{2}, \frac{9}{2}\right) \)

\( =(-1,4.5) \)

Therefore, the coordinates of the required points are \( \left(-3, 1.5\right), (-2,3) \) and \( (-1,4.5) \).

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Updated on: 10-Oct-2022

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