Dividing Line Segments

[shilvastar]

Please help. I've been trying to solve these for more than an hour now but I can't seem to get it.

1) The segment joining (-4,7), (5,-2) is divided into two segments, one of which is 5 times as long as the other. Find the point of division.

2) The segment joining (4,0), (3, -2) is extended each way a distance equal to three times its own length. Find the terminal points.

Please show the solutions so I can study them. Thanks in advance .

 

[Deleted member 4993]

Please help. I've been trying to solve these for more than an hour now but I can't seem to get it.

1) The segment joining (-4,7), (5,-2) is divided into two segments, one of which is 5 times as long as the other. Find the point of division.

2) The segment joining (4,0), (3, -2) is extended each way a distance equal to three times its own length. Find the terminal points.

Please show the solutions so I can study them. Thanks in advance .

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Please share your work with us indicating exactly where you are stuck - so that we may know where to begin to help you.

 

[soroban]

Hello, shilvastar!

1) The segment joining A(-4,7) and B (5,-2) is divided into two segments,
one of which is 5 times as long as the other.
Find the point of division.

Plot the two points; draw the segment joining them.
The point that we want is \(\displaystyle \frac{5}{6}\) of the way from \(\displaystyle A\) to \(\displaystyle B.\)

Going from \(\displaystyle A\) to \(\displaystyle B\), we move 9 units to the right and 9 units down.

Hence, we move: .\(\displaystyle \frac{5}{6}\!\cdot\!9 = \frac{15}{2}\) units right and down.

This places us at: .\(\displaystyle \begin{Bmatrix}x &=& \text{-}4 + \frac{15}{2} &=& \frac{7}{2} \\ y &=& 7 - \frac{15}{2} &=& \text{-}\frac{1}{2} \end{Bmatrix}\)

The point of division is: .\(\displaystyle \left(\frac{7}{2},\:\text{-}\frac{1}{2}\right)\)


Try this technique on the second problem.