Find the coordinates of the vertex -C- of -ABC if its centroid is the origin and the vertices A- B are 1-1-1 and -2-4-1 respectively

→ centroid coordinates: #160; G_x=x_1+x_2+x_33⇒ 0=1 2+c_x3 ⇒ c_x=1 G_y=y_1+y_2+y_33=0=1+4+c_y3⇒ c_y 5 G_z=z_1+z_2+z_33=0=1+1+c_z3⇒ c_ ...

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Standard XII

Mathematics

Centroid of a Triangle

Find the coor...

Question

Find the coordinates of the vertex 'C' of $Δ$ ABC if its centroid is the origin and the vertices A, B are (1,1,1) and (-2,4,1) respectively

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Solution

$\to$ centroid coordinates:
$G_{x} = \frac{x_{1} + x_{2} + x_{3}}{3} \Rightarrow 0 = \frac{1 - 2 + c_{x}}{3}$
$\Rightarrow c_{x} = 1$
$G_{y} = \frac{y_{1} + y_{2} + y_{3}}{3} = 0 = \frac{1 + 4 + c_{y}}{3} \Rightarrow c_{y} - 5$
$G_{z} = \frac{z_{1} + z_{2} + z_{3}}{3} = 0 = \frac{1 + 1 + c_{z}}{3} \Rightarrow c_{z} - 2$
$\Rightarrow c = (1, - 5, - 2)$

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Find the coordinates of the vertex 'C' of ΔABC if its centroid is the origin and the vertices A, B are (1,1,1) and (-2,4,1) respectively

→ centroid coordinates: Gx=x1+x2+x33⇒0=1−2+cx3⇒cx=1Gy=y1+y2+y33=0=1+4+cy3⇒cy−5Gz=z1+z2+z33=0=1+1+cz3⇒cz−2⇒c=(1,−5,−2)

Find the coordinates of the vertex 'C' of $Δ$ ABC if its centroid is the origin and the vertices A, B are (1,1,1) and (-2,4,1) respectively