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Answer:
The coordinated points which quadrasects the line segments joining the points A and B are [tex]\left(-\frac{5}{4},4\right)[/tex], [tex]\left(\frac{1}{2}, 2 \right)[/tex] and [tex]\left(\frac{9}{4},0 \right)[/tex].
Step-by-step explanation:
Let [tex]A(x,y) =(-3,6)[/tex] and [tex]B(x,y) = (4,-2)[/tex], when the line segment is quadrasected, it means that segment is divided into four equal parts. The locations are determined by the following expressions:
[tex]\vec R_{1} = \vec A + \frac{1}{4}\cdot \overrightarrow{AB}[/tex] (1)
[tex]\vec R_{2} = \vec A + \frac{1}{2}\cdot \overrightarrow{AB}[/tex] (2)
[tex]\vec R_{3} = \vec A + \frac{3}{4}\cdot \overrightarrow{AB}[/tex] (3)
Where:
[tex]\overrightarrow{AB} = B(x,y)-A(x,y)[/tex]
[tex]\overrightarrow{AB} = (4,-2) - (-3,6)[/tex]
[tex]\overrightarrow{AB} = (7,-8)[/tex]
The coordinated points which quadrasects the line segments joining the points A and B are, respectively:
[tex]\vec R_{1} = (-3,6)+\frac{1}{4} \cdot (7,-8)[/tex]
[tex]\vec R_{1} = \left(-\frac{5}{4},4\right)[/tex]
[tex]\vec R_{2} = (-3,6)+\frac{1}{2} \cdot (7,-8)[/tex]
[tex]\vec R_{2} = \left(\frac{1}{2},2 \right)[/tex]
[tex]\vec R_{3} = (-3,6)+\frac{3}{4} \cdot (7,-8)[/tex]
[tex]\vec R_{3} = \left(\frac{9}{4},0\right)[/tex]
The coordinated points which quadrasects the line segments joining the points A and B are [tex]\left(-\frac{5}{4},4\right)[/tex], [tex]\left(\frac{1}{2}, 2 \right)[/tex] and [tex]\left(\frac{9}{4},0 \right)[/tex].