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Have to dilate triangle abc by a scale factor of 2 3. And we have have to use point d. As the center of dilation.
Whenever you are performing a that has a fractional scale factor. We should understand that the resulting shape will be smaller than what it was when we started so lets start by figuring out how far away is point a from point d. In the x direction.
We would have to move one two three units to the left. And we would have to move one two three four five six seven eight nine units in the y direction. So what we do is we take those two distances our x distance and our y distance.
And we find two thirds of that distance so instead of going over three units to the left. We take 2 3. Of three which would be 2.
So lets only go two units to the left and instead of going up nine units in the y direction. We are going to take 2 3. Of that distance.
Which would be 6. So lets go up 1 2. 3.
4. 5. 6.
And then were going to label that point point. A. Now lets take a look at where point b.
Is going to be located in the x. Direction. We would have to move 1 2.
3. 4. 5.
To the right. And 1 2. 3.
4. 5. 6.
7. 8. 9.
Up. So were going to take 2 3. Of those dimensions instead of going.
6. To the right were going to do two thirds of that which is 4 to the right. So 1 2.
3. 4. And instead of going up 9 2.
3. Of 9 is 6. So were going to go up 1 2.
3. 4. 5.
6. And then plot our new point. And label.
It point b. And of course point c. Is 1 2.
4. 5. 6.
To the right and 3 up. So once again 2 3. Of 6 is 4.
So we go over to the right 1 2. 3. 4.
And instead of up three. We take 2 3. Of 3.
Which is 2. So we go up 2 units in plot point. See now we can connect our newly formed points to form our dilate triangle.
Lets try another example for this example. We have to dilate triangle abc by a scale factor of 1 2. And once again we have to use point d.
As our center of dilation. So point a is 1 2. 3.
4. 5. Units to the right.
And 1 2. 3. 4.
5. 6. Units above.
What we have to do is take half the distance of five and have the distance of six to determine the new location of 08. Half the distance of five is two and a half so we go to the right one two and a half and instead of going up six. We do half of that distance.
Which is three so we go up 1 2. 3. And then we plot our new point and label.
It point a now for point b. We are going to do something a little bit different the original point b. If you notice is one two three four units to the right and because we are dilating by a scale factor of 1 2.
That means that the new line segment of a b will be one half of its original distance. So instead of b. Being located four units to the right.
Its going to be half of that distance. Which is two units to the right. So lets go to the new location of a and move one two units to the right and then plot our new point.
Which is point b. And originally c. Was located one two three four five six units below.
So we take half that distance. Which is three and plot. The new location of c.
So we are going to go one two three units below and then plot our point and then label it c. And then we can connect our points to form our dilated shape. So we should notice that each corresponding line segment is half the distance of what it was so the new line segment ac.
Is half the distance of the original line segment ac. We should also notice that each new point is half the distance away from the center of dilation than what it was before if you were to draw a line from the center. Dilation and connect it to the new location of a and then keep going to the old location of a we can see that point a or the new point.
A is half the distance of the old point a the same holds true for points b. And points c. As well.
We can clearly see each new point is half the distance of what it was before and that is how you perform a dilation on the coordinate plane when dealing with fractional scale factors you .
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