Question

If (1, 1,1) is the centroid of the traingle with (3, -5, 7) and (-1, 7,-6) as the vertices find the third vertex.​

Answer 1

Answer:

(1,1,2)

Step-by-step explanation:

centroid of a triangle when vertices points are given=

[(X1+X2+X3)/3, (Y1+Y2+Y3)/3,(Z1+Z2+Z3)/3]

as per question, centroid = (1,1,1)

given two points are (3, -5, 7) and (-1, 7,-6).

equating X coordinates in both formula and value of centroid,

===> (X1+X2+X3)/3 =1

===> (3+(-1)+X3)/3 = 1

===> (2+X3) = 3

===> X3= 3-2 =1

so, X3=1.

equating Y coordinates in both formula and value,

===> (Y1+Y2+Y3)/3 = 1

===> (-5+7+Y3)/3 = 1

===> Y3+2=1

so, Y3= -1

equating Z coordinates in both formula and value,

===> (Z1+Z2+Z3)/3 =1

===> (7+(-6)+Z3)/3 = 1

===> 1+Z3=3

so, Z3 =2

so, the third vertex is (1,1,2)

Answer 2

Answer:

Answer:

(1,1,2)

Step-by-step explanation:

centroid of a triangle when vertices points are given=

[(X1+X2+X3)/3, (Y1+Y2+Y3)/3,(Z1+Z2+Z3)/3]

as per question, centroid = (1,1,1)

given two points are (3, -5, 7) and (-1, 7,-6).

equating X coordinates in both formula and value of centroid,

===> (X1+X2+X3)/3 =1

===> (3+(-1)+X3)/3 = 1

===> (2+X3) = 3

===> X3= 3-2 =1

so, X3=1.

equating Y coordinates in both formula and value,

===> (Y1+Y2+Y3)/3 = 1

===> (-5+7+Y3)/3 = 1

===> Y3+2=1

so, Y3= -1

equating Z coordinates in both formula and value,

===> (Z1+Z2+Z3)/3 =1

===> (7+(-6)+Z3)/3 = 1

===> 1+Z3=3

so, Z3 =2

so, the third vertex is (1,1,2)