For any triangle T in the xy–coordinate plan, the center of T is defin

Hi Bunuel,

Great question. The best mode of attack is to Dive In.

Let's start by labeling the three vertices of triangle T as a, b, and c. We know pt a is at (0,0), b is at (6,0), and c is unknown, (cx, cy).

The center, as defined in the problem, is the arithmetic mean of the x and y coordinates individually. Let's write that out as a formula, where the center of triangle T is labeled as pt m at (mx, my).

mx = (ax + bx + cx)/3
my = (ay + by + cy)/3

We know from the problem that pt m is at (3,2), so let's plug in first for the x-coordinate, cx:
3 = (0 + 6 + cx)/3
With some arithmetic, we can solve this to see that cx = 3.

Now, let's do the same for the y-coordinate, cy:
2 = (0 + 0 + cy)/3
So... cy = 6.

Putting these together, we now have that the coordinate of the missing vertex is at (cx, cy), or (3,6)... Answer Choice B.

Hope this helps!

Notice that (3,2) lies on one the median which divides the side connecting [0,0] & [6,0]....and it is give [3,2] is the centre...we know that centriod will divide the median in the ratio 2:1 .....the smaller part of the ratio is 2 here, so the bigger must be 4....and hence the point is [3,6]. Now add the x of all vertices and y of all vertices , find the averages and cross check.

Thus answer B [3,6].

------------
Please give kudos if this helps.

Can I solve this way?

let the vertices be A, B, and C
A=(0,0), B=(6,0), and since the central is (3,2) then C=(3,n)

sum of x=0+6+3=9; avg=9/3=3
sum of y=0+0+n=; avg=n/3=2 (since the center is (3,2))
thus n=3*2=6

So the answer is (3,6) B

Seems like a difficult question , but actually it can be solved in less than 30 seconds.
First plot all the given (X,Y) pair.
You will get the base of the triangle with length of 6 and mid point of triangle at 3,3
Now the vortex will be double at the Y coordinate of the midpoint
Double of 3= 6 (y=3)
Average of X is already 3
Therefore the X,Y pair will become 3,6
Answer is B

The center is 3,2.

Actually the average is of 3 data points, that is why it is 6 because (0+0+y)/3=2 y=6.

X remains at 3 because
(0 + 6 + x) /3 = 3
6+x=9
x=3

At least it made sense to me this way.

Yup , you are right

Average should should be 0+3+6=9/3
= 3
Double of 3=6
so vortex will be (x,y)=(3,6)

I think its a very simple averages question. Median point (3,2) should be equal to {(x1+x2+x3)/3, (y1+y2+y3)/3}.
We have (x1,y1) and (x2,y2) as (0,0) and (6,0).
Thus, 3= (0+6+x3)/3 => x3 = 3
& 2= (0+0+y3)/3 => y3 = 6.
The point, therefore, is (3,6). Option B.

let the co-ordinates of the 3rd vertex be (x,y)

3 = \(\frac{(0+6+x)}{3}\)

x = 3

2 = \(\frac{(0+0+y)}{3}\)

y = 6

Hence the 3rd vertex is (3,6)

niks18 can you pls explain based on what rule do we plug in coordinates of centroid into equation to find third vertex ? i cant undestand logic. We need the coordinates of the last vertex, but we are plugging in corrdinates of centroid thank you

Hi dave13
the question says that the x & y coordinates of the center of triangle is equal to the averages of x & y coordinates of three vertices.
Now you know the average of x coordinate and you know two x coordinates of the vertices, you need to find out the 3rd x coordinate
Similarly for y coordinate.
Take this question as an average question and try to solve

3 = (0 + 6 + x)/3
x = 9 - 6 = 3

2 = (0 + 0 + y)/3
y = 6

Therefore, 3rd Vertex = (3, 6) => B

I got it right and thought this was such an easy question but I am confused after seeing the replies.

My method:

X coordinate of 3rd vertex:

3= (0+6+x)/3......... because average.
x=3.

Y coordinate of 3rd vertex:

2= (0+0+y)/3......... because average.
y=6.

Thus, 3rd vertex is (3,6)

Is this a valid method or I was just lucky? Bunuel

Nothing but a word problem: need to realize the wording and basics of arithmetic mean.

Posted from my mobile device