## Constructing a Dilation 128-3.12

this video is provided as supplementary material for courses taught at Howard Community College and in this video I'm going to demonstrate how to construct a dilation of an image so we're going to start with the image of this triangle triangle ABC I'm going to dilate it by a scale factor of 2 and I'll use point P as the center of dilation so the first step is going to be to draw array starting at point P and going through point a so use a straightedge for that I'll draw that ready I'll continue quite a ways then I'm going to take my compass and set it so it's the same distance as line segment PA and with a point of the compass over to point a and draw an arc along the line so with that arc intersects the line is twice as far from point P as point a was so I've dilated that line by a scale factor of 2 so that's going to be that point there where the arc intersects the line is going to be point a prime of my dilated image now we'll repeat that process two more times for each of the other points on the original image so I'll draw array starting at Pig and going through point B I'll set a compass equal to the distance for line segment PB move the point of the compass over to point B draw an arc where the arc intersects the line is now going to be point B Prime and one more time this time the Rays going to start at line say at Point P and go through Point C take the compass set it for the length of line segment PC and repeat that length with an arc that's going to get me point C Prime and now for my new image all I have to do is connect points a prime B Prime and C Prime so there's line segment a prime C prime B prime B prime and B prime C Prime so triangle a prime B prime C prime is a dilated image of triangle ABC I used to scale factor of 2 and the center of dilation was at Point P that's it take care I'll see you next time

## Constructing a Parallel Line Through a Given Point 128-2.21

this video is provided as supplementary material for courses taught at Howard Community College and in this video I'm going to demonstrate how to construct a parallel line through a given point using a compass and a straightedge there are a number of methods for doing this here's the one I'm going to use I've drawn a line which I'm calling line ail and above the line I've got point P what I want to do is draw a line through point P that is parallel to L now here's how I'm going to do it I'm going to place a point on line L I'll call that point a and you can put this point just about anywhere then I'm going to draw a line through points a and pig now that line that I've just drawn creates an angle at a my next step is going to be to copy that angle over to point P so I'll do this by placing my compass point on point a and drawing an arc that goes through those two lines and then I'll copy that I place in the compas point on pig and drug another arc and now I'm going to copy the angle at a by setting my compass equal to the distance between where the arc touches each of those two lines now I copy that distance onto my second arc and now I can create a parallel line by connecting point P where the place where these two arcs intersect now I've got a line which is parallel to my first line here's how I know they're parallel I've got two lines and transversal that's the second line that I drew the corresponding angles angle a and angle P are congruent if that's the case those two lines have to be parallel lines so now I know that I've drawn a line parallel to line L to point P okay that's it take care I'll see you next time