Question

Can someone help me here, please?

Consider a triangle ABC. Given the vertex A=(4,1), the AB midpoint M=(2, -1) and the barycentre G=(-2,0), find the vertexes B and C.

Well, through a graph I managed to find B=(0,-3). Then I thought about using the formula Barycentre(X)=(X(a) + X(b) + X(c))/3
Which would be like -2 = (4 + 0 + X(c))/3 and X(c)=-10, but my book says C=(-4, 1/2). Where did I go wrong?

Answer 1

Could you give me a quick explanation of what the barycentre is?

Answer 2

the gravity point of a triangle

Answer 3

http://www.brasilescola.com/upload/e/baricentro.JPG

Answer 4

So then informally, your barycentre should be the average value of your triangle

Answer 5

What do you mean?

Answer 6

I mean that your formula makes sense in an informal way, so I believe that it's correct.

I'm also getting -10 for the x-value of C. In fact, if you graph it, an x-value of -4 makes very little sense.

Answer 7

They seem to entirely discounting the point A for their calculation of the x-coordinate. What are you getting for the y-coordinate?

Answer 8

I'm getting y = 2

Answer 9

Same here.

Answer 10

My book must be wrong then

Answer 11

Thanks

Answer 12

You're welcome.