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If the points A (6, 1), B (8, 2), C (9, 4) and D (k, p) are the vertices of a parallelogram taken in order, then find the values of k and p.

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Our given vertices are A(1, -2), B(3, 6) and C(5, 10) and fourth vertex be D(k, p) 

It is given that quadrilateral joining these four vertices is parallelogram, ie □ABCD is parallelogram. 

We know that diagonals of parallelogram bisect each other, ie midpoint of the diagonals coincide.

 Let E(xm , ym) be the midpoint of diagonals AC and BD.

By midpoint formula,

For diagonal BD,

\(\frac{15}2\) = \(\frac{8+k}2,\frac{5}2\) = \(\frac{p+2}2\)

∴ k = 15 – 8 , y = 5 – 2 

∴ k = 7 and p = 3 

Hence, 

our fourth vertex is D(7 , 3)

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