Show that (-3, 2), (-5, -5), (2, -3) and (4, 4) are the vertices of a rhombus.

The points A(-3, 2), B(-5, -5), C(2, -3) and D(4, 4) are the vertices of a quadrilateral. We need to show that this quadrilateral is a rhombus. Distance between the given points = Distance between points A(-3, 2) and B(-5, -5): Distance between points B(-5, -5) and C(2, -3): Distance between points C(2, -3) and D(4, 4): Distance between points D(4, 4) and A(-3, 2): AB = BC = CD = DA = Since all sides are equal, the quadrilateral is a rhombus. Hence, the points (-3, 2), (-5, -5), (2, -3) and (4, 4) are the vertices of a rhombus.

Find the value of k, if the points (5, k) and (k, 7) are equidistant from point (2, 4).

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Points A (-3, -2), B (-6, a), C (-3, -4) and D(0, -1) are the vertices of quadrilateral ABCD; find a if 'a' is negative and AB = CD.

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The vertices of a triangle are (5, 1), (11, 1) and (11, 9). Find the co-ordinates of the circumcentre of the triangle.

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Mathematics

Show that (-3, 2), (-5, -5), (2, -3) and (4, 4) are the vertices of a rhombus.

Distance Formula

Related Questions

Find the value of k, if the points (5, k) and (k, 7) are equidistant from point (2, 4).

Points A (-3, -2), B (-6, a), C (-3, -4) and D(0, -1) are the vertices of quadrilateral ABCD; find a if 'a' is negative and AB = CD.

The vertices of a triangle are (5, 1), (11, 1) and (11, 9). Find the co-ordinates of the circumcentre of the triangle.