Question

If a vertex of a parallelogram is (1,2) and the diagonal cut at (3,5), Find the opposite vertex???​

Answer 1

Step-by-step explanation:

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Answer 2

First of all we find out if given vertices are adjacent or opposite vertices of the parallelogram.

If these are opposite vertices then the intersection point (2,-5) should be the mid point of the diagonal joining vertices (3,2) & (-1,0). But its mid point is (1,1). Mid point can be calculated by section formula. So givenvertices can not be opposite.

=> given vertices are adjacent vertices.

Now, we calculate the vertex opposite to ( 3,2)

Since diagonals bisect each other. So the intersection point (2,-5) should be the mid point ie m1:m2 = 1:1

Hence third vertex by section formula

2 = (3+x)/2 => x = 1

-5 = (2+y)/2 => y =-12

=> third vertex = ( 1,-12) . . . . . . . . Ans

4th vertex ,opposite to (-1,0) by section formula

2= (-1 +x)/2 => x= 5

-5 = (0 + y)/2 => y= -10

=> fourth vertex = (5,-10). . . . . . . . . .Ans

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