Answer :
Given: the points A(a, -11), B(5, b), C(2, 15) and D(1, 1) are the vertices of a parallelogram ABCD.
To find: the values of a and b.
Solution:
Given points are A(a, -11), B(5, b), C(2, 15) and D(1, 1) and let the intersection of diagonals be E(xm , ym )
It is given that □ABCD is a parallelogram.
By midpoint formula.
x = , y =
We know that midpoint of parallelogram coincide.
∴ Midpoint of AC = Midpoint of BD
∴ ( ,
) = (
,
)
∴ =
and
=
⇒ a + 2 = 6 and 4 = b + 1
⇒ a = 6 - 2 and 4 - 1 = b
∴a = 4 and b = 3
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