About this video
Sal dilates triangle ABC about center P with scale factor 1/4. For each vertex he counts how far it is from P horizontally and vertically, multiplies those distances by 1/4, and plots the new point. For example, C is 8 left and 4 up from P, so C' is 2 left and 1 up.
You'll be able to
- explain what a scale factor less than 1 does in a dilation.
- dilate a point by multiplying its horizontal and vertical distances from the center by the scale factor.
Key words
- dilation
- A transformation that scales a figure up or down from a center point.
- center of dilation
- The fixed point that all distances are measured and scaled from.
- scale factor
- The number distances from the center are multiplied by; 1/4 makes them a quarter as long.
Transcript
- [Instructor] We're told 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.
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