If centroid of the triangle formed by 9,a b,-4 and 7,8 is 6,8 find a and b
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Step-by-step explanation:
Given:
The co-ordinates of the centroid of the triangle (6,8)
And the co-ordinates of the three vertices of the triangle (9,a), (b,-4), and (7,8).
Required to find:
The value of a and b
Solution:
Since Centroid of the triangle is given by ((x₁ + x₂ + x₃)/3, (y₁ + y₂ + y₃)/3)
∴(x₁ + x₂ + x₃)/3 = 6
⇒(9 + b + 7)/3 = 6
⇒(9 + b + 7) = 18
⇒b +16 = 18
⇒b = 2
And,
(y₁ + y₂ + y₃)/3 = 8
⇒(a - 4 + 8)/3 = 8
⇒a + 4 = 24
⇒a = 20
∴ Value of a = 20 and b = 2
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