Similar triangles & slope: proportion using coordinates
About this video
Triangles DEF and DKL are similar right triangles on one line. Sal reads the given slope calculation as (y1 - y2)/(x1 - x2) using F(8, -3) and D(-7, 9), then completes the proportion for the smaller triangle by using L(3, 1) with the same point D, giving (1 - 9)/(3 - (-7)), which is choice D.
You'll be able to
- identify the points used in a slope calculation written with coordinates.
- write a slope as (y1 - y2)/(x1 - x2) for two points.
- complete a proportion showing two similar slope triangles have equal slopes.
Key words
- slope
- Change in y over change in x between two points on a line.
- coordinates
- A pair of numbers (x, y) that gives a point's position on a grid.
- similar right triangles
- Right triangles with the same shape, so their side ratios are equal.
- proportion
- An equation stating two ratios are equal.
Transcript
- [Instructor] We're told that triangle D-E-F, D-E-F, and triangle, D-K-L, D-K-L, are similar right triangles. Complete the proportion to show that the slope of D-F, so that's this segment right over here, D-F, equals the slope of D-L. So pause this video and see if you could 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 and so 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. And so 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. X1, now you know it's equal to 8. And it looks like Y2... Remember you subtract Y2. So Y2 is 9 and it looks like X2, X2 is -7. So it looks like they're trying to get, find the slope, between the points 8, -3 and the point -7, 9. So let's see what points those are.
So 8, -3, 8, -3 is this one right over here. So 8, -3 is point F right over there. And then -7, 9,
- 7, 9 is point D right over there. So 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.
So then 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 minus 9, so that's the same Y2 for D. And then X1 here is 3 minus X2. X2 for D we've already seen is -7, minus 7. So let's see which of those choices are that.
So if I look at that, that's exactly what we wrote right over here in choice D.
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