MAY BE DISTANCE AND SECTION FORMULA BE ALSO USED IN THIS SUM

Using distance formula, we have:

AB = ?(-5+1)² + (4+2)² = ?16 + 36 =?52

BC = ?(-1-5)² + (-2-2)² = ?36 + 16 =?52

CA = ?(-5-5)² + (4-2)² = ?100 + 4 =?104

Now, AB = BC and AB² + BC² = CA²

Hence, the given vertices are the vertices of an isosceles right triangle.

 

Since, ABCD form a square, AC = BD

(The diagonals of a square are equal)

Therefore, AC² = BD²

Now, apply the distance formula to find AC² and BD² and then equate both to get a relation between x and y.                 (1)

Also, all sides of a square are of equal length.

So, AB = AD

This will give you another relation between x and y.             (2)

 

Solve the two relations/equations to get the value of x and y and hence to get the coordinates of point D.