the centroid of a triangle is (2,. 7, -1) and two of its vertices are (4, 8, ,2) and (-2, 6, 3) the third vertex is?
Answers
Answer:
Let
A
(
4
,
8
)
and
B
(
−
2
,
6
)
be the given vertex. Let
C
(
h
,
k
)
be the third vertex.
The centroid of
Δ
A
B
C
is
(
4
−
2
+
h
3
,
8
+
6
+
k
3
)
It is given that the centroid of triangle ABC is
(
2
,
7
)
.
∴
4
−
2
+
h
3
=
2
,
8
+
6
+
k
3
=
7
⇒
h
=
4
,
k
=
7
Thus, the third vertex is
(
4
,
7
)
Given : The centroid of a triangle is (2,7,-1) and two of its vertices are (4,8,2) and (-2,6,3)
To Find : the third vertex
Solution:
vertices are (4,8,2) and (-2,6,3)
and third vertex (x , y , z)
Centroid
= (4 -2 + x)/3 , ( 8 + 6 + y)/3 , (2 + 3 + z)/3
= (x + 2)/3 , ( y + 14)/3 , ( z + 5)/3
Centroid is (2,7,-1)
=> (x + 2)/3 = 2 => x = 4
( y + 14)/3 = 7 => y = 7
( z + 5)/3 = - 1 => z = -8
Third vertex is (4 , 7 , - 8)
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