Worksheets · Geometry

Partitioning a directed line segment worksheet

To split the segment from A to B in the ratio m:n, go the fraction m/(m + n) of the way from A toward B, in x and in y separately.

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Sigma Prep · sigmaprep.io/worksheets

Name

Partitioning a Segment

Date Period

Find each point.

  1. Partition a directed segment

    A=(−8,0), B=(4,−8). Find the point that divides the directed segment from A to B in the ratio 3:1.
  2. A=(5,−4), B=(2,−10). Find the point that divides the directed segment from A to B in the ratio 2:1.
  3. A=(−3,−1), B=(−6,5). Find the point that divides the directed segment from A to B in the ratio 1:2.
  4. A=(3,7), B=(18,2). Find the point that divides the directed segment from A to B in the ratio 2:3.
  5. A=(−2,−3), B=(4,0). Find the point that divides the directed segment from A to B in the ratio 1:2.
  6. A=(−8,8), B=(−17,11). Find the point that divides the directed segment from A to B in the ratio 1:2.
  7. A=(−2,1), B=(−11,−8). Find the point that divides the directed segment from A to B in the ratio 1:2.
  8. A=(5,−8), B=(−3,−4). Find the point that divides the directed segment from A to B in the ratio 3:1.
  9. A=(2,0), B=(−7,−3). Find the point that divides the directed segment from A to B in the ratio 2:1.
  10. A=(6,7), B=(−3,13). Find the point that divides the directed segment from A to B in the ratio 1:2.

  1. Find the missing endpoint

    P is 12 of the way from A to B(−6,−5), and P=(−4,−5). Find A.
  2. P is 34 of the way from A(−4,−6) to B, and P=(−1,−6). Find B.
  3. P is 25 of the way from A(4,−2) to B, and P=(2,0). Find B.
  4. P is 25 of the way from A(−4,7) to B, and P=(−4,13). Find B.
  5. P is 34 of the way from A(7,−4) to B, and P=(1,−7). Find B.
  6. P is 13 of the way from A to B(13,0), and P=(9,4). Find A.
  7. P is 25 of the way from A to B(−7,−2), and P=(−1,1). Find A.
  8. P is 13 of the way from A to B(3,5), and P=(3,−1). Find A.
  9. P is 25 of the way from A(2,1) to B, and P=(−4,−3). Find B.
  10. P is 14 of the way from A(1,4) to B, and P=(4,4). Find B.

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Partitioning a SegmentAnswer keyVersion 1

Date Period

Find each point.

  1. Partition a directed segment

    A=(−8,0), B=(4,−8). Find the point that divides the directed segment from A to B in the ratio 3:1.(1,−6)
  2. A=(5,−4), B=(2,−10). Find the point that divides the directed segment from A to B in the ratio 2:1.(3,−8)
  3. A=(−3,−1), B=(−6,5). Find the point that divides the directed segment from A to B in the ratio 1:2.(−4,1)
  4. A=(3,7), B=(18,2). Find the point that divides the directed segment from A to B in the ratio 2:3.(9,5)
  5. A=(−2,−3), B=(4,0). Find the point that divides the directed segment from A to B in the ratio 1:2.(0,−2)
  6. A=(−8,8), B=(−17,11). Find the point that divides the directed segment from A to B in the ratio 1:2.(−11,9)
  7. A=(−2,1), B=(−11,−8). Find the point that divides the directed segment from A to B in the ratio 1:2.(−5,−2)
  8. A=(5,−8), B=(−3,−4). Find the point that divides the directed segment from A to B in the ratio 3:1.(−1,−5)
  9. A=(2,0), B=(−7,−3). Find the point that divides the directed segment from A to B in the ratio 2:1.(−4,−2)
  10. A=(6,7), B=(−3,13). Find the point that divides the directed segment from A to B in the ratio 1:2.(3,9)

  1. Find the missing endpoint

    P is 12 of the way from A to B(−6,−5), and P=(−4,−5). Find A.(−2,−5)
  2. P is 34 of the way from A(−4,−6) to B, and P=(−1,−6). Find B.(0,−6)
  3. P is 25 of the way from A(4,−2) to B, and P=(2,0). Find B.(−1,3)
  4. P is 25 of the way from A(−4,7) to B, and P=(−4,13). Find B.(−4,22)
  5. P is 34 of the way from A(7,−4) to B, and P=(1,−7). Find B.(−1,−8)
  6. P is 13 of the way from A to B(13,0), and P=(9,4). Find A.(7,6)
  7. P is 25 of the way from A to B(−7,−2), and P=(−1,1). Find A.(3,3)
  8. P is 13 of the way from A to B(3,5), and P=(3,−1). Find A.(3,−4)
  9. P is 25 of the way from A(2,1) to B, and P=(−4,−3). Find B.(−13,−9)
  10. P is 14 of the way from A(1,4) to B, and P=(4,4). Find B.(13,4)

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

A=(1,2), B=(10,8), ratio 1:2

  1. The point is 1/3 of the way from A to B.
  2. x: 1 + (1/3)(9) = 4; y: 2 + (1/3)(6) = 4.

The answer is (4,4).

Where students go wrong

Using m/n instead of m/(m + n). A ratio of 1:2 cuts the segment into three parts, so the point is a third of the way, not half.

Also called directed line segment, dividing a segment in a ratio or section formula.

What you can put on this worksheet

Partitioning a directed segment
A=(1,4), B=(−5,7). Find the point that divides the directed segment from A to B in the ratio 1:2. → (−1,5)
The other endpoint, from a point part way along
P is 14 of the way from A(1,4) to B, and P=(−2,4). Find B. → (−11,4)

Questions about these worksheets

Yes. Every partitioning a directed line segment sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Geometry is usually taken around 9th or 10th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the partitioning a directed line segment questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 2: partitioning a directed segment and the other endpoint, from a point part way along. Tick as many as you want and set how many of each, or let it spread them evenly.

Using m/n instead of m/(m + n). A ratio of 1:2 cuts the segment into three parts, so the point is a third of the way, not half.