What are the coordinates of the point on the directed line segment from (-10, 3)(−10,3) to (-7, -3)(−7,−3) that partitions the segment into a ratio of 2 to 1?

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02-04-2020
Mathematics

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What are the coordinates of the point on the directed line segment from (-10, 3)(−10,3) to (-7, -3)(−7,−3) that partitions the segment into a ratio of 2 to 1?

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profantoniofonte profantoniofonte · Answer 1 · 2020-04-03T03:39:09+02:00

Answer:

P(-8,-1)

Step-by-step explanation:

1) Let's visualize the coordinates points on the Cartesian Plane.

(Check it out)

2) Directed Segments are line segments with direction and length, i.e. a starting point. The starting point of a directed segment may start in A or B.

3) When we make partitions into a ratio of 2 to 1, this is to say we'll divide the line segment in three parts the first one will have twice the size of the later one.

The Point that indicates the partition is called P.

If we calculate the distance of the segment

[tex]d=\sqrt{(-3-3)^{2}+(-10+7)^{2} } \\ d\cong 6.71[/tex]

So, that's the length of the line segment AB

4) Let's find P

Firstly let's divide AB into three segments. [tex]\frac{1}{3}\overline {AB}=\frac{1}{3}*3\sqrt{5} =\sqrt{5} \cong 2.23[/tex]

Since the Partition Ratio is 2:1

[tex]AP=2\sqrt{5} =4.46[/tex]

[tex]PB =\sqrt{5}=2.24[/tex]

Now, let's trace a perpendicular line down the point A.

Just as the graph below

P (-8,-1)