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
Science Fiction Inspires the Future of Science | National Geographic
The wonders of the future, the marvels of the presence. Science fiction and science innovation have been intertwined since sci-fi’s origins. From video chat to self-driving cars to space flight, there’s the science fiction and the science reality. Sci-fi …
Introduction to production functions | APⓇ Microeconomics | Khan Academy
You will hear the term production function thrown around in economics circles, and it might seem a little intimidating and a little mathy at first. But as you’re about to see, it’s a fairly basic idea. It’s this idea that you could have these various inp…
Last Wild Places: Iberá | National Geographic
(Inspirational music) (Thunder rolls) [Sebastián] Iberá was a place that was degraded by humans. And it’s a place that is being recovered by humans. It’s an incredible example of what we can achieve if we have the decision of restoring an ecosystem on a …
Tidepooling along the Pacific Coast | National Geographic
Nature, the most powerful creative force on Earth. I’m Chef Melissa King. Cooking has taken me to incredible places. Magical. (laughs) From TV competitions and celebrity galas to countries around the world, I’m heading out to places I’ve never been before…
Emergence – How Stupid Things Become Smart Together
An ant is pretty stupid. It doesn’t have much of a brain, no will, no plan, and yet, many ants together are smart. An ant colony can construct complex structures. Some colonies keep farms of fungi; others take care of cattle. They can wage war or defend t…
Ruchi Sanghvi on Sweating the Details
So after about a year of working on Cove, it was the best year ever because I learned the most. Cove was acquired by Dropbox. We wanted to build at scale, and Dropbox gave us a bigger stage to do just that. We loved the people, and we loved the product, a…