(529)

Given,

The equations of two adjacent sides of a parallelogram ABCD be 2x-3y = -23 and 5x + 4y = 23,

So, AB 2x - 3y = -23 and BC 5z + 4y = 23

Also given, AC 3x + 7y = 23

Solving the above lines we get, A(-4, 5), B(-l, 7), C(3, 2)

We know that,

Diagonal of parallelogram have same midpoint,

So AC and BD have same mid-point and let point D be (x,y),

So midpoint formula we get,

and

Hence, point D is (0, 0)

Now Equation of BD will be 7x + y = 0

Now finding the distance of A(-4, 5) from 7x + y = 0 we get,

Hence, 50d 2 = 23 2 = 529

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