The co-ordinates of the centroid of a triangle ABC are (3,−2). What are the co-ordinates of vertex C if co-ordinates of A and B are (−2,5) and (6,−2) respectively?
- A(-5,-9)
- B(5,-9)
- C(5,9)
- D(-5,9)
Solution & Step-by-step Explanation
Let the coordinates of vertex C be (x
3
,y
3
).
Given coordinates:
A=(x
1
,y
1
)=(−2,5)
B=(x
2
,y
2
)=(6,−2)
Centroid G=(x,y)=(3,−2)
The formula for the coordinates of the centroid is:
x=
3
x
1
+x
2
+x
3
,y=
3
y
1
+y
2
+y
3
For the x-coordinate:
3=
3
−2+6+x
3
9=4+x
3
x
3
=5
For the y-coordinate:
−2=
3
5+(−2)+y
3
−6=3+y
3
y
3
=−9
Thus, the coordinates of vertex C are (5,−9).
3
,y
3
).
Given coordinates:
A=(x
1
,y
1
)=(−2,5)
B=(x
2
,y
2
)=(6,−2)
Centroid G=(x,y)=(3,−2)
The formula for the coordinates of the centroid is:
x=
3
x
1
+x
2
+x
3
,y=
3
y
1
+y
2
+y
3
For the x-coordinate:
3=
3
−2+6+x
3
9=4+x
3
x
3
=5
For the y-coordinate:
−2=
3
5+(−2)+y
3
−6=3+y
3
y
3
=−9
Thus, the coordinates of vertex C are (5,−9).