# Show that the points A(0, 6), B(2, 1) and C(7, 3) are three corners of a square ABCD. Find (i) the slope of the diagonal BD and (ii) the coordinates of the fourth vertex D.

In a square, all sides are perpendicular to the adjacent side, so the product of slope of two adjacent sides is -1.

Let the position of point D(a,b).

Given points of the square are A(0, 6),B(2, 1),C(7, 3) and D(a,b).

The slope of line AB =

The slope of line BC =

The slope of line CD =

The slope of line DA =

The slope of diagonal AC =

The slope of diagonal BD = m5

(i) We know that in a square, two diagonals are perpendicular to each other, therefore

The slope of diagonal AC×slope of diagonal BD = -1

So the slope of diagonal BD is 7/3.

(ii) We know that midpoint of diagonal AC = midpoint of diagonal BD

and comparing x and y coordinates respectively.

So coordinate of the point D(5,8).

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