1. Simplify and verify your result for a=1 and b=-1 a?b(a'-a+1)-ab(a-2a? +2a)-bla-3-1)
2.Simplify -3/2a(2a-3b+4c)+9/2 and find its value for a=1,b=-1 and c=-2.
3.Simplify :(3a-2)(a-1)(3a+5)
4. Multiply (2x2+3x-5) by (3x?-5x+4)
5.Simplify (5x+3a)(5x-3a)+(2x-5a)(x+5a)
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Answer:
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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