Show that the points (2, 1), (0, 3), (-2, 1) and (0, -1), taken in order, are the vertices of a square. Also find the area of the square.

Let A(2, 1), B(0, 3), C(-2, 1) and D(0, -1) be the four points. By distance formula, Since, AB = BC = CD = AD i.e. all sides are equal so, ABCD can be a rhombus or a square. Calculating diagonals, Since, diagonals are equal. ∴ ABCD is a square. Area of square = (side) 2 = (AB) 2 = = 8 sq. units. Hence, proved that (2, 1), (0, 3), (-2, 1) and (0, -1), taken in order, are the vertices of a square and area = 8 sq. units.

If A(-3, 2), B(α, β) and C(-1, 4) are the vertices of an isosceles triangle, prove that α + β = 1, given AB = BC.

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The ends of a diagonal of a square have co-ordinates (-2, p) and (p, 2). Find p if the area of the square is 40 sq. units.

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Prove that the points (3, 0), (6, 4) and (-1, 3) are the vertices of a right angled isosceles triangle.

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Show that the points (-3, 2), (-5, -5), (2, -3) and (4, 4), taken in order, are the vertices of rhombus. Also, find its area. Do the given points form a square?

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Mathematics

Show that the points (2, 1), (0, 3), (-2, 1) and (0, -1), taken in order, are the vertices of a square. Also find the area of the square.

Coordinate Geometry

Related Questions

If A(-3, 2), B(α, β) and C(-1, 4) are the vertices of an isosceles triangle, prove that α + β = 1, given AB = BC.

The ends of a diagonal of a square have co-ordinates (-2, p) and (p, 2). Find p if the area of the square is 40 sq. units.

Prove that the points (3, 0), (6, 4) and (-1, 3) are the vertices of a right angled isosceles triangle.

Show that the points (-3, 2), (-5, -5), (2, -3) and (4, 4), taken in order, are the vertices of rhombus. Also, find its area. Do the given points form a square?