Misal P titik tengah AC AP : PC = 1 : 1 AP/PC = 1/1 (p - a)/(c - p) = 1/1 p - a = c - p 2p = a + c p = (a + c)/2 = (-2+1, 1+(-7))/2 = (-1, -6)/2 = (-1/2, -3) Jadi titik P (-1/2, -3)
D titik berat sehingga PD : DB = 1 : 2 PD/DB = 1/2 (d - p)/(b - d) = 1/2 2d - 2p = b - d 3d = 2p + b 3d = 2(-1/2, -3) + (4, 3) 3d = (-1, -6) + (4, 3) 3d = (-1+4, -6+3) 3d = (3,-3) d = (3,-3)/3 = (1,-1) Jadi koordinat titik D = (1,-1)
Cara cepat D = ((x1+x2+x3)/3, (y1+y2+y3)/3) = ((-2+4+1)/3, (1+3+(-7))/3) = (3/3, -3/3) = (1,-1)
Misal P titik tengah AC
AP : PC = 1 : 1
AP/PC = 1/1
(p - a)/(c - p) = 1/1
p - a = c - p
2p = a + c
p = (a + c)/2 = (-2+1, 1+(-7))/2 = (-1, -6)/2 = (-1/2, -3)
Jadi titik P (-1/2, -3)
D titik berat sehingga PD : DB = 1 : 2
PD/DB = 1/2
(d - p)/(b - d) = 1/2
2d - 2p = b - d
3d = 2p + b
3d = 2(-1/2, -3) + (4, 3)
3d = (-1, -6) + (4, 3)
3d = (-1+4, -6+3)
3d = (3,-3)
d = (3,-3)/3 = (1,-1)
Jadi koordinat titik D = (1,-1)
Cara cepat D = ((x1+x2+x3)/3, (y1+y2+y3)/3)
= ((-2+4+1)/3, (1+3+(-7))/3) = (3/3, -3/3) = (1,-1)