Question

find four vertex of the parallelogram if three of its vertices are given as A (10,-2) B (8,6) and C(6,10)​

Answer 1

Answer:

(8,2)

Step-by-step explanation:

We know that the diagonals of a parallelogram bisect each other. Hence the lines AC and BD (diagonals) will have a common midpoint O.

By Midpoint Theorem-

O (x,y) = (10+6)/2, (-2+10)/2

⇒ O (x,y) = (8,4)

Now, (8+x)/2, (6+y)/2 = (8,4)

On comparing LHS and RHS -

(8+x)/2 = 8                                    and               (6+y)/2 = 4

⇒ x = 8                                                           ⇒ y = 2

Hence the fourth vertex is (8,2).

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