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Geometry Video Series: Finding the Centroid

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well hello everybody and welcome to our video series 4 chapter 4 this is the first video of 4 videos this is coordination and this is a processor please understand that could these problems be solved by using coordinate geometry and using a horse always work when that doesn't work and you have to grind out the problems this is where coordinate geometry comes into place that we want to find the centroid of triangle ABC 868 B's -3 and 3 C's at 2 and -3 so what is first step is to get the graph so I can graph paper draw it out go ahead and find your midpoints afterwards so here's triangle a b and c I found the midpoints that when you find the midpoint formula or you can count the rise over the Run doesn't really matter what ahead and found the midpoint of X tubing of a be at X or at 1.5 and 5.5 family point of BC and CA and you can see that midpoint of AC is a z e r and Z is at 4 and 2.5 in the midpoint of BC is that why we're negative points 5 and 0 again you can use the midpoint formula or you can just count the rise over the Run let's follow this concept here because the midpoints the vertices of the triangle when connected are called medians and so if we want to find where these medians meet do we need to look at all three or just two of them well think about it we only need to find two of them so I'm going to look for the equation of each of these medians again I can look but it's two of them that's the first thing you have to get a slope airports near formula y minus y1 equals m * x - x 1 all right so here's a so I'm going to go ahead and connect point a to its midpoint here across the way all right so it's fine the line for that well I had the slope of a y is at 8 / 6.5 there's the formula crank out the algebra and you should get an equation for that line a y 16 or 13 x + 8 / 13 2 intersect this medium take a look that's fine a why so go ahead and repeat the process all right this is for your outdoor skills really come in handy so I'm going to take a look at mine b c so line be easy would be right here all right so now this point right here Define is the intersection of my two medians what I'm looking for repeat the process align final line of be easy as y equals 8 1/14 x + 39 / 14 and now for systems equation and for that I'm going to make my lines a y equal to line easy so you can see we only have one variable variable X find crank out the algebra again and we find that x equals 5/3 go ahead and plug in 5/3 back into one of the original equations and we find that y equals 1/3 therefore let's see this is about let's see where is the centroid really at there we go the centuries at 5/3 and 8/3 there and their please understand that this is a process that there's a lot of algebra as you can see we have for steps one by your graph find your midpoints three on the equation the lights for the median in this case and four systems of equations I hope that helps thank you

Uploaded by Nello Santillana.

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Geometry Video Series: Finding the Centroid

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