For any triangle T in the xy-coordinate plane

[agha79]

For any triangle T in the xy-coordinate plane, the center of T is defined to be the point whose x-coordinate is the average (airthmetic mean) of the x-coordinates of the vertices of T and whose y-coordinate is the average of the y-coordinates of the vertices of T. if a certain triangle has vertices at the points (0,0) and (6,0) and center at the point (3,2), what are the coordinates of the remaining vertex?

A- (3,4)
B- (3,6)
C- (4,9)
D- (6,4)
E- (9,6)

I searched for the question in the form but was unable to find it. Can anyone please provide detail explanation? I don’t even know where to start here.

OA: B

[kartikeya.payautomata]

hi there

this is an easy question and the question is simply for finding the centroid of a triangle
to begin with consider the third unknown vertice to be (x,y)
so avg of all x cordinates of the triangle vertices should be equal to 3 as it is given 3 is the x cordinate of the center
therefore (0+6+x)/3=3
so x=3 is the required x cordinate same is for y cordinate
(0+0+y)/3=2
on solving y=6

hence the cordinates are (3,6)

so b

[agha79]

I am sorry but have a dumb question. Why average needs to be 3. May be I am missing some basic rule here

[RonPurewal]

agha79 - it says so in the problem.

For any triangle T in the xy-coordinate plane, the center of T is defined to be the point whose x-coordinate is the average (airthmetic mean) of the x-coordinates of the vertices of T and whose y-coordinate is the average of the y-coordinates of the vertices of T. if a certain triangle has vertices at the points (0,0) and (6,0) and center at the point (3,2), what are the coordinates of the remaining vertex?

red stuff: the average of 0, 6, and unknown x is 3.

blue stuff: the average of 0, 0, and unknown y is 2.

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you can also solve this by just plugging in the answer choices, if you don't feel like doing algebra. just plug the choices in, and see which one gives the required average.