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### Course: Geometry (all content)>Unit 15

Lesson 2: Dividing line segments

# 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?
• 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.
• Is there a common formula, for these types of sums?
• Yes, (x,y) = (x1 + k(x2-x1), y1 + k(y2-y1)) where k is the fraction: part/whole.
• 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!
• 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.
• At could somebody better explain why parallel line components(x, y length) have the same ratio as the line lengths?
• 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.
• How can I use this in a science career?
• 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!
• 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.
• 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). At in 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.
• 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