three consecutive vertices of parallelogram (3,0);(5,2);(-2,6) find the fourth vertex
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Answer:
We have,
A(x
1
,y
1
)=(3,0)
B(x
2
,y
2
)=(5,2)
C(x
3
,y
3
)=(−2,6)
Let AC be the diagonal of rectangle
Then,
Let middle point of Diagonal is (x,y)
(x,y)=
2
x
1
+x
3
,
2
y
1
+y
3
(x,y)=(
2
3+(−2)
,
2
0+6
)
(x,y)=(
2
1
,3)
Let the fourth vertex of rectangle is D and its coordinate is (x
4
,y
4
)
So, BD is the diagonal of its rectangle.
Then,
(x,y)=(
2
x
2
+x
4
,
2
y
2
+y
4
)
(
2
1
,3)=(
2
5+x
4
,
2
2+y
4
)
2
1
=
2
5+x
4
,3=
2
2+y
4
5+x
4
=1,6=2+y
4
x
4
=−4,y
4
=4
Hence, the fourth vertices is find
This is a rectangle.
Step-by-step explanation:
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