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# Dilations and properties

CCSS.Math:

## Video transcript

what we're going to do in this video is think about how shapes properties might be preserved or not preserved from dilations and so here we have this quadrilateral and we're going to dilate it about point P here and I have this little dilation dilation tool so the first question is are the coordinates of the vertices going to be preserved well pause the video and try to think about that well now let's just try it out experimentally we can see under an arbitrary dilation here the coordinates are not preserved the point that corresponds to D has is now has a different coordinate the vertices the vertex that corresponds to a now has different coordinates same thing for B and C the corresponding points after the dilation now sit on a different part of the coordinate coordinate plane so in this case the coordinates of the vertices are not preserved now the next question let me go back to where we were so the next question the corresponding line segment after a dilation are they sitting on the same line and so let me dilate again and so you can see if you consider this point B prime because it corresponds to point B the segment B prime C prime this does not sit on the same line as BC but the segment a prime D prime the corresponding line segment to line segment ad that does sit on the same line and if you think about it why that is well if we originally draw a line that if we look at the line that contains segment ad it also goes through point P and so as we expand out this segment right over here is going to expand and shift outward along the same lines but that's not going to be a true of these other segments because they don't because the point P does not sit on the line that that those segments sit on and so let's just expand it again so you see that right over there now the next question our angle measures preserved well it looks like they are and this is one of the things that is true about a dilation is that you're going to preserve angle measures this angle is still a right angle this angle here the I guess you could call it angle the measure of angle B is the same as the measure of angle B Prime and you can see it with all of these points right over there and then the last question are side lengths perimeter an area preserved well we could immediately see as we dilate outwards for example the segment corresponding to a D has gotten longer in fact if we dilate outwards all of the segments the corresponding segments are getting larger and if they're all getting larger then the perimeter is getting larger and the area's getting larger likewise if we dilate in like this they're all getting smaller so side lengths perimeter and area are not preserved now let's ask the same questions with another dilation and this is going to be interesting because we're going to look at a dilation that is centered at one of the vertices of our shape so let me scroll down here and so I have the same tool again and now here we have a triangle triangle ABC and we're going to dilate about Point C so first of all do we think the vertices the coordinates of the vertices are going to be preserved let's dilate out well you can see Point C is preserved it when it gets mapped after the dilation it sits in the exact same place but the things that correspond to a and B are not preserved you could call this a prime and this definitely has different coordinates than a and B prime definitely has different coordinates than B now what about corresponding line segments are they on the same line well some of them are and some of them aren't so for example when we dilate so look at let's look at the segment AC and the segment BC when we dilate we can see whoops when we dilate we can see the corresponding segment you could call this a prime C prime or B prime C prime do still sit on that same line and that's because the point that we are dilating about Point C sat on those original segments so we're essentially just lengthening out on on the point that is not the center of dilation we're lengthening out away from it or if the dilation is going in we would be shortening along that same line but some of the segments are not overlapping on the same line so for example a prime B prime does not sit along the same line as a B now what about the angle measures well we already talked about it angle measures are preserved under dilations the measure of angles see here this is the exact same angle and so is the measure of angle you could call this a prime and B prime right over here and then finally what about side lengths well you can clearly see that when I dilate out my side lengths increase or if i dilate in my side lengths decrease and so side lengths are not preserved and a side lengths are not preserved then the perimeter is not preserved and also the area is not preserved you could view area as a function of the side lengths if we dilate out like this the perimeter grows and so does the area if we dilate in like this the perimeter shrinks and so does the area