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Question

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


A
(3,32),(2,3),(1,92)
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B
(3,12),(1,3),(1,92)
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C
(2,1),(1,3),(1,12)
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D
(1,2),(2,3),(1,12)
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Solution

The correct option is A $$\left ( -3, \dfrac{3}{2} \right ) , (-2, 3), \left ( -1, \dfrac{9}{2} \right )$$
Given points are A(-4, 0) and B(0, 6)
Mid-point of A and B will be (x, y), then $$\displaystyle x = \frac{-4 + 0}{2} =-2$$
and $$\displaystyle y = \frac{0+6}{2} = 3$$, therefore mid-point is (-2, 3).
Now mid-point of (-4, 0) and (-2. 3) will be
$$x_1 = \frac{-4-2}{2} = -3$$  and $$y_1 = \frac{0+3}{2} = \frac{3}{2} i.e., \left (-3,  \frac{3}{2} \right )$$
Again mid-point of (-2, 3) and (0, 6) will be
$$x_2 = \frac{-2 + 0}{2} =-1    and    y_2 = \frac{3+6}{2} = \frac{9}{2} i.e.,  \left ( -1, \frac{9}{2} \right )$$
Therefore three points are $$\left ( -3, \frac{3}{2} \right ), (-2, 3), \left ( -1, \frac{9}{2} \right )$$

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