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

Scaling perimeter and area example 2 | Transformational geometry | Grade 8 (TX) | Khan Academy

2m read
·Nov 10, 2024

We're told quadrilateral A was dilated by a scale factor of 2/3 to create quadrilateral B. Complete the missing measurements in the table below. So like always, pause this video and then we will do this together. Try to do it yourself, and then we'll do it together.

All right, so in previous videos, we talked about if you have a scale factor, perimeter is going to be scaled by the same amount, while area is going to be scaled by the square of that. So perimeter is also going to be scaled by 2/3. So 30 * 2/3… let me write that a little bit neater. So times 2/3 is going to be 20.

Then the 54 is going to be scaled by (2/3) squared. One way to think about it is, you're scaling in each dimension by 2/3, and so when you multiply the two dimensions to get area, you're going to be multiplying by 2/3 twice to get the new scaled area. So what is (2/3) squared? Well, that is the same thing as 4/9. So what is 54 * (4/9)?

That is equal to 54 * (4 over 9). Both 54 and 9 are divisible by 9, so let's divide them both by 9. This becomes 6, and this becomes 1. So we end up with 6 * 4, which is equal to 24, and we're done.

Now to make this very tangible in your head, let's give an example of where this could actually happen. Let's imagine that quadrilateral A, let's say it looked like this, and I think I can eyeball it. Let's say that that dimension is 6, and that dimension is 9. I think that adds up: 6 plus 6 is 12, and 9 plus 9 is 18. So yes, this perimeter is 30, and the area here is actually 54.

So this is actually the example of quadrilateral A over here. And now quadrilateral B, if we're scaling it by 2/3, then all of these dimensions are going to be scaled by 2/3. So quadrilateral B will, instead of having a length of—or height of—6 over here, it's going to have a height of 4, and instead of having a length or width of 9 here, it's going to be 2/3 of that. It's going to be 6.

So the quadrilateral will look like this, and we can verify that the perimeter now is going to be 4 plus 4, which is 8, plus 6, plus 6, which is 12. So it's 8 plus 12, which is 20, and the new area is 6 * 4, which is 24. Now, you didn't have to do this, but I just wanted to make sure you understood why this was happening.

Mr. Freeman, part 04
The Most Iconic TAG Heuer Watch of All Time | Monaco Split-Seconds Chronograph

More Articles

View All
Becoming a Millionaire: Roth IRA vs 401K (What makes the MOST PROFIT)
What’s up, guys? It’s Graham here. So, here’s a question that’s been coming up a lot recently, and this is a very confusing question for most people. That is this: What is better to invest in, a Roth IRA or traditional 401k? Now, this is actually a some…
Indus Valley Civilization | Early Civilizations | World History | Khan Academy
As we’ve talked about in multiple videos, some of the earliest civilizations we have found have been around river valleys, and that is no coincidence. Because some of the first agriculture emerged around river valleys, and the agriculture supported higher…
Introduction to residuals and least-squares regression | AP Statistics | Khan Academy
Let’s say we’re trying to understand the relationship between people’s height and their weight. So what we do is we go to 10 different people and we measure each of their heights and each of their weights. And so on. This scatter plot here, each dot repr…
Introduction to nucleic acids and nucleotides | High school biology | Khan Academy
We are now going to talk about what is perhaps the most important macromolecule in life, and that is known as nucleic acid. Now, first of all, where does that name come from? Well, scientists first observed this in the nucleus of cells, and so that’s wher…
Worked example: Rewriting definite integral as limit of Riemann sum | AP Calculus AB | Khan Academy
Let’s get some practice rewriting definite integrals as the limit of a Riemann sum. So let’s say I wanted to take the definite integral from π to 2π of cosine of x dx. What I want to do is write it as the limit as n approaches infinity of a Riemann sum. …
Dave Bautista Makes a Log Ladder | Running Wild With Bear Grylls
[music playing] So the terrain here is definitely getting steeper and more committing. But you know, so much of survival is about just trying to be resourceful. I just wonder if maybe we maybe use that old trunk. Use that, get that down, and then we can d…