Finding the unknown points of a second triangle

[Will15]

Homework Statement

Triangle A has three points a(2,3)b(0,0)c(2,0) and its center is (2/3,1). Find the other three points of Triangle B with a center of (4/3,3).

Homework Equations

Center of a triangle:
x = ax+bx+cx /3
y = ay+by+cy / 3

Magnitude = <a,b> , √(a^2+b^2)

The Attempt at a Solution

1)Obtaining the vector of AB by subtracting the two center <4/3-2/3, 3-1> = <2/3,2>
2)Magnitude of vector AB is (2*√10)/3
3)Adding the magnitude to the three points of triangle A
4)Check answer by calculating the center with the 3 new points, should match with the given center above.

Step 4 is where I'm stuck, I can't get the same x center.

 

[Mark44]

Homework Statement

Triangle A has three points a(2,3)b(0,0)c(2,0) and its center is (2/3,1). Find the other three points of Triangle B with a center of (4/3,3).

Homework Equations

Center of a triangle:
x = ax+bx+cx /3
y = ay+by+cy / 3

Magnitude = <a,b> , √(a^2+b^2)

The Attempt at a Solution

1)Obtaining the vector of AB by subtracting the two center <4/3-2/3, 3-1> = <2/3,2>
2)Magnitude of vector AB is (2*√10)/3
3)Adding the magnitude to the three points of triangle A
4)Check answer by calculating the center with the 3 new points, should match with the given center above.

Step 4 is where I'm stuck, I can't get the same x center.

How is triangle B related to triangle A?

 

[Will15]

How is triangle B related to triangle A?

The relation is unknown.