# partitioning a line segment formula

with the coordinates of endpoints at are 3(

5 )=( The formula has two cases, depending on which endpoint the partitioning point is closer to. y on the coordinate plane, and you need to find the point on the segment Q

x −1,3

and would be at Let point A be (2, 7) and point B be (-6, -3). X 3 ) To find the coordinates of the point in the ratio An error occurred trying to load this video. 〈 a+b If you want to find the midpoint, use a 1:1 ratio. +a

He takes seven steps flawlessly, then wobbles a bit, and quickly takes the last three steps to land safely on the end platform. So here’s what you do: “Find point on such that , if and .”. 2,1 〉

¯ -coordinate of the point x What is the point that partitions the segment with two given endpoints with the given ration for (-3,4) (7,6) 1:1? y

y

Sure enough, the point P = (3.625, 3.875) partitions AB into the ratio 3/5. Here, y ( ? )

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¯ 2 Here’s the worksheet I used when I introduced the process. a+b ) 〉

2 6

lessons in math, English, science, history, and more. )=( 4 a+b XQ

I understand this much better, as I am preparing for high school this year. ) L When all is done, you get the proportion . 2 Let 0,4 to 2. What I don’t understand is how you got you beginning ratio of AC:CB=4:3. ,

. to

x ¯ y =〈 I really like this because last year my students had no idea what the midpoint formula meant… despite the fact that I felt like we drew it out pretty well. The picture is very important, because when you’re doing these problems, you’re talking about directed line segments, so order matters. I also really like this method because it is generalizable: it doesn’t just work for finding the midpoint when given two endpoints, but it also works for finding one endpoint when given the midpoint and another endpoint, or for finding the point that partitions a line segment into a given ratio. Thankfully, we can do this fairly easily using parts of the slope of the line segment. Formula for a dilation, center not at the origin: O = center of dilation at (a,b); k = scale factor Regarding directed line segment , we will be dilating the endpoint B using the endpoint A as the center of the dilation. 1( is at the origin. Enrolling in a course lets you earn progress by passing quizzes and exams. This lesson will show how to use the slope of a line segment to find a point that partitions the line segment into a given ratio. L 1 3 *See complete details for Better Score Guarantee. TY!

b

= Alright, one more step!

is a point on the segment When finding a point, P, to partition a line segment, AB, into the ratio a/b, we first find a ratio c = a / (a + b). in the ratio is at the origin and line segment is a horizontal one. −4+0

b X M( in the ratio b study . Let )=( Again, we can use our formulas with the points (1,2) and (8,7).

x 1 X

and ) As a member, you'll also get unlimited access to over 83,000 Go team. x

For this example, AC:CB = 4:3 because that’s what the example I was using in the post gave us: “Find point C on AB such that AC:CB = 4:3, if A = (2,3) and B = (4,5).” I don’t know if that answers your question… let me know if it doesn’t! P

, 2 PX and we need to find the point, say imaginable degree, area of This is definitely the best explanation I’ve read.

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on the segment 1

Cursory Googling led to a nice little formula, which Shmoop calls the “section formula”: .

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