Main content

### Course: Geometry (Eureka Math/EngageNY) > Unit 4

Lesson 4: Topic D: Partitioning and extending segments and parameterization of lines# Dividing line segments

Watch Sal figure out the coordinates of a point between two other points that give a certain ratio. Created by Sal Khan.

## Want to join the conversation?

- For our endpoint, C, we received the coordinates (4, -6). I noticed these two numbers were the same as the change in x and the change in y. Is this just a coincidence or is there a correlation?(50 votes)
- That was highly coincidental. Shift the entire line 1 unit to the right on the x-axis and that will no longer be the case. The change in x and change in y are still the same, but we end up at (5, -6) instead.(57 votes)

- Is there a common formula, for these types of sums?(19 votes)
- Yes, (x,y) = (x1 + k(x2-x1), y1 + k(y2-y1)) where k is the fraction: part/whole.(42 votes)

- I really hope somebody can help.

In the last video the ratio was 3:1 and Sal broke it up into 4 parts (3+1). However, in this video he broke it up into 5 parts and used it as a fraction. That confuses me. If anyone can help, then that would be great!(19 votes)- Sal broke up the ratio in the previous video because the ratio for that problem was between segments AB and BC. In this problem, the ratio is between segments AB and AC.(19 votes)

- At2:05could somebody better explain why parallel line components(x, y length) have the same ratio as the line lengths?(13 votes)
- Try drawing the changes in x and y so that you have two overlapping right triangles (with AB and AC as the hypotenuses). You'll see that the triangles are similar (by angle-angle-angle), so the corresponding sides have the same ratio.(26 votes)

- How can I use this in a science career?(4 votes)
- Depending on what you actually do, geometry is used in analyzing data for experiments or setting up experimental conditions. Logical thinking is exercised by geometry. Like a weight lifter or gymnast, thinkers need exercise too. Exercising your mind is important in scientific work. Believe me (I am a scientist -- physics and chemistry), I see a lot of people that desperately need mental exercise!(33 votes)

- Can somebody explain which coordinate point to subtract/add to when the differences are found? When I do the problems sometimes it's subtracted by A and others by B, so I'm confused.(14 votes)
- I think that it depends on how you count the units. For example, when you count right to left, the answer you will get the opposite of getting left to right (1 is opposite of -1). At1:57in the video, Sal counts from left to right, letting him get a positive distance. To make things less complicated, you could use absolute value to get positive numbers for distances. Despite the different ways to count, you still should get the same answer either way.(3 votes)

- the point of this video is to show how to divide line segments without a graph, THE FIRST THING YOU SAY IS GET A GRAPH(16 votes)
- At3:13, did Sal just invert and multiply? Also can I cross multiply and then transfer the 4 to divide the other side by 4?(12 votes)
- I
*cannot*get the problems in the practice exercise. The word**ratio**scares me half to death, and my brain freezes. I don't really know how to do ratios. Does anyone have some tips on how to divide line segments?(11 votes) - Anyone else here doing their summer homework?(9 votes)
- We're in the same boat, HackerTyper10. I'm actually skipping a grade this year, and I happen to be using Khan Academy for math.(5 votes)

## Video transcript

- [Instructor] We're told point A is at negative one comma four and point C is at four common negative six. Find the coordinates of point
B on segment, line segment AC such that the ratio of AB
to AC is three to five. So pause this video and see
if you can figure that out. All right, now let's work
through this together and to help us visualize,
let's plot these points. So first, let us plot point A which is at negative one comma four. So negative one comma
one, two, three, four so that right over there is point A and then let's think about point C which is at four common negative six. So one, two, three,
four, comma negative six, negative one, negative
two, negative three, negative four, negative five,
negative six, just like that and so the segment AC, I
get my ruler tool out here. Segment AC is going to look like that and the ratio between
the distance of A to B and A to C is three to five or another way to think about it is B is going to be three fifths along the way from A to C. Now the way that I think about it is in order to be three fifths
along the way from A to C you have to be three fifths
along the way in the X direction and three fifths along the
way in the Y direction. So let's think about
the X direction first. We are going from X equals
negative one to X equals four to go from this point to that point. Our change in X is one,
two, three, four, five and so if we wanna go
three fifths of that, we went a total of five,
three fifths of that is going just three. So that is going to be B is X coordinate and then we can look on
the Y coordinate side. To go from A to C, we are
going from four to negative six so we're going down by
one, two, three, four, five, six, seven, eight, nine, 10 and so three fifths of 10 would be six. So B's coordinate is going to be one, two, three, four, five, six down. So just like that, we
were able to figure out the X and the Y coordinates for point B, which would be right over here and you could look at
this directly and say, look, B is going to be
have the coordinates. This looks like this is
two comma negative two which we were able to do the graph paper. So another way you could think
about it even algebraically is the coordinates of B,
we could think about it as starting with the coordinates of A so negative one comma four, but we're gonna move
three fifths along the way in each of these dimensions towards C. So it's going to be
plus three fifths times how far we've gone in the extraction. So in the extraction to go from A to C, you were going from negative one to four and so that distance is
four minus negative one and this of course is
going to be equal to five and then on the Y dimension,
this is going to be our A's Y coordinate plus three fifths times the distance that we
travel in the Y direction and here we're going from
four to negative six. So we say negative six minus
four, that is negative 10 and so the coordinates of
B are gonna be negative one plus three fifths times five
is going to be plus three and then four plus three
fifths times negative 10, well, three three fifths
negative 10 is negative six. and so that gets us two comma
negative two and we are done, which is exactly what
we got right over there.