Question

Let the opposite angular points of square be (3,4) and(1,-1). Find the coordinates of remaining angular points.

Answer 1

Let A(3, 4) and C(1, -1) be the given angular points of the square ABCD and let B(x, y) be the unknown vertex.

Then, AB = BC

AB2 = BC2

(x-3)2 + (y-4)2 = (x+1)2 + (y-1)2

This gives x =Double click to edit

Also, AB2 + BC2 = AC2

Using distance formula, find an equation from the above relation and then substitute the value of x from equation (1) in the obtained equation. That will give the values for y. Find the corresponding values of x.

The points (x, y) will be the required two angular points of the square.

Hope my answer got it.