yego.me
💡 Stop wasting time. Read Youtube instead of watch. Download Chrome Extension

Similar triangles & slope: proportion using coordinates | Grade 8 (TX) | Khan Academy


2m read
·Nov 10, 2024

We're told that triangle DF and triangle DKL are similar right triangles. Complete the proportion to show that the slope of DF, so that's this segment right over here DF, equals the slope of DL. So pause this video and see if you can complete it. They started the proportion here, and so this is going to be equal to one of these choices.

All right, now let's do this together. So the first thing I want to do is I just want to figure out what they're trying to calculate here. We already know that we are dealing with slope. Let me get the right tool out, that we're dealing with slope. This looks like a slope calculation right over here, and we know slope is change in y over change in x, which you could view as y1 minus y2 over x1 minus x2.

When I look at the points that are used here, it looks like y1 is that point right over there, or it's -3. X1 is 8; well, I know it's equal to 8. It looks like y2—remember, you subtract y2—so y2 is 9, and it looks like x2 is -7. So it looks like they're trying to find the slope between the points (8, -3) and the point (-7, 9).

So let's see what points those are. (8, -3) is this one right over here; so (8, -3) is point F right over there. Then (-7, 9) is point D right over there. If you want to do the same thing for this smaller triangle, you would still use point D as the second point, but you would use point L as the first point.

So point L right over here is the point (3, 1). So essentially, let's do the same calculation, where this is x1 and y1, and we're going to use the same x2 and y2 as before. If we did that, we are going to get—so on the numerator, y1 is 1 minus y2, which is y2 for D; so that's -9. That's the same y2 for D, and then x1 here is 3 minus x2. x2 for D we've already seen is -7.

So let's see which of those choices are that. If I look at that, that's exactly what we wrote right over here in Choice D.

More Articles

View All
Capital by Thomas Piketty | Macroeconomics | Khan Academy
Thomas Piketty’s Capital in the 21st Century has been getting a lot of attention lately because it’s addressing an issue that matters a lot to a lot of folks: the issue of income inequality and wealth inequality. My goal here isn’t to have a view on the b…
How to sell a private jet!
8:00 a.m. Tuesday morning. Our business is truly international across every time zone. During those few hours I spend sleeping, deals, texts, emails, and calls build up, so I spend most of every morning catching up. Today we’re on our way to the Air Chart…
Chi-square test for association (independence) | AP Statistics | Khan Academy
We’re already familiar with the chi-squared statistic. If you’re not, I encourage you to review the videos on that. And we’ve already done some hypothesis testing with the chi-squared statistic. We’ve even done some hypothesis testing based on two-way tab…
Miami Is Sinking | Explorer
How do we know climate change has happened? Well, the first thing is with the glaciers. Glaciers are receding; the world’s getting warmer. People have written computer models of the atmosphere. You imagine boxes of air, boxes of water, and you make them …
Graphing logarithmic functions (example 2) | Algebra 2 | Khan Academy
This is a screenshot from an exercise on Khan Academy. It says the interactive graph below contains the graph of y is equal to log base 2 of x as a dashed curve, and you can see it down there is that dashed curve with the points (1, 0) and (2, 1) highligh…
Warren Buffett: How Most People Should Invest
[Music] So Warren Buffett, we know he is the world’s best investor, and he has built his fortune by analyzing individual businesses and buying them at discounted prices. His strategy can essentially be summarized by just waiting and waiting and waiting un…