Analytic Geometry

A square is a quadrilateral with four equal sides. The area of a square is equal to square of its sides. The diagonal of a square is a line segment joining any two non-consecutive side. Find the area of a square and the length of its diagonal whose vertices are (3,1), (-1,5), and (-1,-3). Draw the square.

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  1. (-1,5) and (-1,-3) are the ends of a vertical line. Since (3,1) is not at the same y-coordinate as either of those, the vertical line must be a diagonal. It has length=8.

    Since the diagonal has length 8, its sides have length 4√2, giving an area of 32.

    Knowing that the other diagonal is horizontal and has length=8, it should be easy to plot the missing vertex and draw the square.

    For what it's worth, the diagonal is a line segment joining two non-consecutive vertices, not sides.

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