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### Course: Integrated math 1>Unit 18

Lesson 2: Dividing line segments

# Dividing line segments: graphical

Watch Sal figure out the coordinates of a point between two other points that give a certain ratio. A graph is given to make it easier to visualize the problem. Created by Sal Khan.

## Want to join the conversation?

• at , i don't understand how you got 1/4 for the ratio 3:1?

i've been doing the lesson this video is for in geometry for awhile now, and the others don't make sense to me either. i started to think it was just getting them to 4:4, since 1 + 3 = 4 and since there was already a 4 in 1/4, you just made it a 1 in 3:1.

but that doesn't always work. for example, problems with the starting ratio of 3:4 for AB had another one of 3:7 or 3/4. i just don't get it.
• I'll try to clarify, I am studying Geometry myself but I would like to help :)

First, let's start with an example using ratios. Say that a cookie recipe said that the ratio between flour and sugar is 3:1 cups. That means for every 3 cups of flour, there is 1 cup of sugar. After you add 3 cups of flour and 1 cup of sugar in, you just added in 4 total cups of ingredients! So, if I need to add 3 cups of flour and 1 cup of sugar, and I start by adding 1 single cup of flour, I am now 1/4 finished with putting the ingredients in (because I still need to add 2 more cups of flour and 1 sugar).

Although using this example for this situation may be a bit more confusing, it still works. Like Sal said at , the longer part of the line segment is three times as large (or 3x, as he states it) than the smaller part, x. It's like how we add 3 times as much flour than sugar in the cookie recipe. Now that we know CB is x, and BA is 3x, we can say x + 3x, or x+x+x+x, equals 4x, or 4 units. So, CB is 1/4.

I hope this helped! XD
• How can we get the soution mathematically?
• is there a way to understand what fraction to use? Why dont we just use the ratio? How do we use the ratio to find the fraction to use in our equation? what if the numbers are different,say 3:4 instead of 3:1, is the fraction then 1/7? I dont understand.
• This one is a little tricky on the first go. The reason they use "1/4" is because a 3:1 ratio is 3 to 1 distance on the line segment given. On a 3:4 ratio, the fraction would would be "3/7", because it would be 3 parts out of 7 total parts on the line segment.

Hope this could clarify!
• can i ask what formula will usefor finding ratio?
thanks
• How do I tell if it wants me to do C vertical to A horizontal and vice versa because its so confusing
• So each point has an x coordinate and a y coordinate. You want to first look at one and then the other. So if you first look at the x coordinates, you can see that the total length is 16 (the two points are sixteen dashes apart on the x axis). Then you look at the y coordinates for both points, and see the total height is 5 (the points are five dashes apart when looking at the y axis.

We know the ratio is 3:1, so since 3 + 1 equals 4, we want to divide these numbers into four parts. 16 divided into four parts is 4. And 4 divided into four parts is 1. We want the line AB to have 3 of the parts and the line BC to have one of the parts. That will make the line AB to be three times as long as BC.

So if we start at point C, we want to count up 1 and over 4 to get point B. Or we could start at point A and count down 3 and to the left 12. Either way, you get point B in the same place and create a line AB which is three times as long as BC (so point B is 1/4 the distance of the line of AC).
• how does this make sense?
• Where did you get 1/4 from?
• How is it that point B is 1/4th of the way across point A and C? Is it because the whole thing is 4?
• It's 1/4 of the way from point C to point A. This is because the ratio of AB to BC is 3 to 1. And if you want to convert a ratio to a fraction, you need to take the 1 for the numerator and then add the two together for the denominator. I hope this helped! I'm gonna include Grace's answer to a similar question. Mabye it'll explain it a little more.
I'll try to clarify, I am studying Geometry myself but I would like to help :)

First, let's start with an example using ratios. Say that a cookie recipe said that the ratio between flour and sugar is 3:1 cups. That means for every 3 cups of flour, there is 1 cup of sugar. After you add 3 cups of flour and 1 cup of sugar in, you just added in 4 total cups of ingredients! So, if I need to add 3 cups of flour and 1 cup of sugar, and I start by adding 1 single cup of flour, I am now 1/4 finished with putting the ingredients in (because I still need to add 2 more cups of flour and 1 sugar).

Although using this example for this situation may be a bit more confusing, it still works. Like Sal said at
, the longer part of the line segment is three times as large (or 3x, as he states it) than the smaller part, x. It's like how we add 3 times as much flour than sugar in the cookie recipe. Now that we know CB is x, and BA is 3x, we can say x + 3x, or x+x+x+x, equals 4x, or 4 units. So, CB is 1/4.

I hope this helped! XD
Me again:
I hope this helps! Please do let me know if it doesn't! :)
• I don't understand the ratios part, I've got an exercise where they say 5:6 is 🟥🟥🟥🟥🟥🟦 5/6 or 1/6, but the guy on this video says 3:1 is 🟥🟥🟥🟦 3/4 or 1/4
• OK, to clarify, lets use marbles. Image you have a box of 11 marbles, 5 red, 6 blue. The ratio would be 5 red : 6 blue. Here, the video says there are 4 marbles, 3 red, 1 blue. The blue one is 1/4th of the total marbles. Hope this helped =D

P.S: The guy narrating the video is Sal Khan.