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प्रश्न
A(h, –6), B(2, 3) and C(–6, k) are the co–ordinates of vertices of a triangle whose centroid is G (1, 5). Find h and k.
उत्तर
A(x1,y1) = A(h, -6),
B (x2 , y2) = B(2, 3),
C (x3 , y3) = C (-6, k)
∴ centroid G (x, y) = G (1, 5)
G is the centroid.
By centroid formula,
x = `("x"_1 + "x"_2 + "x"_3)/3`
∴ 1 = `(h + 2 +(-6))/3`
∴ 3 = h + 2 - 6
∴ 3 = h – 4
∴ h = 3 + 4
∴ h = 7
y = `("y"_1 + "y"_2 + "y"_3)/3`
∴ 5 = `(-6 + 3 + "k")/3`
∴ 15 = -3 + k
∴ k = 15 + 3
∴ k = 18
∴ h = 7 and k = 18
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