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)