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

Dilating shapes: shrinking | Performing transformations | High school geometry | Khan Academy


2m read
·Nov 10, 2024

  • [Instructor] We're told to draw the image of triangle ABC under a dilation whose center is P and scale factor is 1/4.

And what we see here is the widget on Khan Academy where we can do that. So we have this figure, this triangle ABC, A, B, C, right over here, and what we wanna do is dilate it. So that means scaling it up or down, and the center of that dilation is this point P.

So one way to think about it is let's think about the distance between point P and each of these points, and we wanna scale it by 1/4. So the distance is going to be 1/4 of what it was before.

So, for example, this point right over here, if we just even look diagonally from P to A, we can see that we are crossing one square, two squares, three squares, four squares. So if we have a scale factor of 1/4, instead of crossing four squares diagonally, we would only cross one square diagonally.

So I'll put the corresponding point to A right over there. Now, what about for point C? It's not quite as obvious, but one way we could think about it is we can think about how far are we going horizontally from P to C, and then how far do we go vertically? So horizontally, we're going one, two, three, four, five, six, seven, eight of these units, and then vertically we're going one, two, three, four.

So we're going to the left eight and up four. Now, if we have a scale factor of 1/4, we just multiply each of those by 1/4. So instead of going to the left eight, we would go to the left two. Eight times 1/4 is two. Instead of going up four, we would go up one.

So this would be the corresponding point to point C. And then we'll do the same thing for point B. When we go from P to B, we're going one, two, three, four, five, six, seven, eight up, and we're going four to the left.

So if we have a scale factor of 1/4, instead of going eight up, we'll go two up, and instead of going four to the left, we'll go one to the left. So there you have it. We have just dilated triangle ABC around point P with a scale factor of 1/4, and we are done.

More Articles

View All
It Started: Housing Prices Are Collapsing
What’s up guys? It’s Graham here. So, we’ve got some bad news for the housing market, and unfortunately, it’s expected to get a lot worse. That’s because a new report just found that nearly 10 percent of homes purchased in the last nine months are now ups…
Introduction to electron configurations | AP Chemistry | Khan Academy
In a previous video, we’ve introduced ourselves to the idea of an orbital. Electrons don’t just orbit a nucleus the way that a planet might orbit a star, but really, in order to describe where an electron is at any given point in time, we’re really thinki…
Playing in the Mud Never Gets Old for These Two Cave Explorers | Short Film Showcase
Doesn’t go anywhere. See those two holes there? I pushed the hoenn for a meter and a half, and it’s mad all the way. Okay, I was gonna say, with only no shot for three years, and that’s why I still hang out. We’re trying to connect the junior cave system…
HOW TO WATCH THE ECLIPSE (AND SHADOW SNAKES) - Smarter Every Day 171
Hey, it’s me Destin, welcome back to Smarter Every Day. We’ve all heard about solar eclipses, right? And you’re probably aware that there’s a huge one coming very soon. So, you think about how to prepare, and you’re thinking maybe I gotta get some special…
Introduction to residuals and least squares regression
So I’m interested in finding the relationship between people’s height in inches and their weight in pounds. I’m randomly sampling a bunch of people, measuring their height, measuring their weight, and then for each person, I’m plotting a point that repres…
How Geographic Realities Keep Russia's Economy Behind
Two Russian-dominated multinational empires succeeded one another on the same territory, the first being called candidly the Russian Empire and the second the Soviet Union. Geographically, Russia is in some ways like the rest of Eastern Europe, but its na…