Question

Find the coordinated points which quadrasects the line segments joining the points A(-3,6) and B (4,-2)

Answer 1

The coordinated points which quadrasects the line segments joining the points A and B are
`\left(-(5)/(4),4\right)`,
`\left((1)/(2), 2 \right)` and
`\left((9)/(4),0 \right)`.

Explanation:

Let
`A(x,y) =(-3,6)` and
`B(x,y) = (4,-2)`, when the line segment is quadrasected, it means that segment is divided into four equal parts. The locations are determined by the following expressions:

`\vec R_(1) = \vec A + (1)/(4)\cdot \overrightarrow{AB}` (1)

`\vec R_(2) = \vec A + (1)/(2)\cdot \overrightarrow{AB}` (2)

`\vec R_(3) = \vec A + (3)/(4)\cdot \overrightarrow{AB}` (3)

Where:

`\overrightarrow{AB} = B(x,y)-A(x,y)`

`\overrightarrow{AB} = (4,-2) - (-3,6)`

`\overrightarrow{AB} = (7,-8)`

The coordinated points which quadrasects the line segments joining the points A and B are, respectively:

`\vec R_(1) = (-3,6)+(1)/(4) \cdot (7,-8)`

`\vec R_(1) = \left(-(5)/(4),4\right)`

`\vec R_(2) = (-3,6)+(1)/(2) \cdot (7,-8)`

`\vec R_(2) = \left((1)/(2),2 \right)`

`\vec R_(3) = (-3,6)+(3)/(4) \cdot (7,-8)`

`\vec R_(3) = \left((9)/(4),0\right)`

The coordinated points which quadrasects the line segments joining the points A and B are
`\left(-(5)/(4),4\right)`,
`\left((1)/(2), 2 \right)` and
`\left((9)/(4),0 \right)`.