(-7, -3), (5, 10), (15,8) and (3,-5) are the vertices of a .... taken in order.
1) Parallelogram 2) Rectangle
3) Rhombus 4) Square
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Answer:
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D(3,2)
Step-by-step explanation:
Sol. Let A(1,−2), B(3,6) and C(5,10) be the three vertices of a parallelogram ABCD and let its fourth vertex be D(a,b).
Join AC and BD. Let AC and BD intersect at point O.
We know that the diagonals of a parallelogram bisect each other.
So, O is the midpoint of AC as well as that of BD.
Using Midpoint formula X=(
2
x
1
+x
2
)and Y=(
2
y
1
+y
2
)
A(1,−2)≡(x
1
,y
1
), C(5,10)≡(x
2
,y
2
)
Midpoint of AC is (
2
1+5
,
2
−2+10
), i.e.,(3,4)
Midpoint of BD is (
2
3+a
,
2
6+b
)
∴
2
3+a
=3 and
2
6+b
=4
3+a=6 and 6+b=8
a=3 and b=2
Hence, the fourth vertex is D(3,2).
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