Question

If the centroid of a triangle with vertices (7,a),(9,10) and (b,-6) is the point (6,3), find the value of a and b.

Answer 1

6=(7+9+b)/3. , 3=(a+10-6)/3
18=16+b. , 9=4+a
b=2. , a=5
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Answer 2

Answer:

a = 5 and b = 2

Step-by-step explanation:

Let the vertices be A(7,a) ; B(9,10); C(b,-6).  And let the centroid be O(6,3)

If the coordinates of the centroid are (x,y) and the coordinates of the vertices are (x1,y1) ; (x2,y2) ; and (x3,y3) , then the coordinates of the centroid will be

x = (x1+x2+x3) ÷ 3

∴ 6 = (7 + 9 + b) ÷ 3

18 = 16 + b

∴b= 2

and y coordinate will be

y = (y1 + y2 + y3) ÷ 3

3 = ( a + 10 - 6) ÷ 3

9 = a + 4

a = 5

∴a = 5

and b = 2

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