Answer the following. Show that the points (-2,2),(13,10),(21,-5), and (6,-13) are the vertices

step 1 Okay, so we are discussing the distance formula and we have show that the points negative 2 -2,

Answer the following. Show that the points...

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Key Concepts

Distance Formula

The distance formula, based on the Pythagorean theorem, is used to compute the distance between two points in the coordinate plane by taking the square root of the sum of the squares of the differences in their x- and y-coordinates. It is a key tool in determining the lengths of sides when verifying the properties of geometric figures.

Properties of a Rhombus

A rhombus is a quadrilateral with all four sides equal in length. Additionally, its diagonals are perpendicular bisectors of one another, which is another distinguishing characteristic. These properties are critical when proving that a given set of points forms a rhombus.

Coordinate Geometry Verification

Using coordinate geometry, one can verify the nature of a polygon by calculating distances and examining relationships such as slopes and midpoints. This approach allows for an algebraic check of properties like equal side lengths and perpendicular intersections of diagonals, which is particularly useful in identifying specific quadrilaterals such as a rhombus.

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