The following set of coordinates represents which figure? (-5 ,2), (-3, 4), (1, 0), (-1, -2)
a) Kite b) Rectangle c) Rhombus d) Square

Solution:

We know that

A Kite is a quadrilateral where exactly two pairs of adjacent sides are equal.

A rectangle is a quadrilateral where opposite sides are equal.

A square and rhombus are quadrilaterals in which all sides are equal.

The set of coordinates given are

A(-5, 2), B(-3, 4), C(1, 0), D(-1, -2)

We have to find the figure represented by the set of coordinates.

Distance between the points is given by

Distance = \(\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}\)

AB = \(\sqrt{(-3-(-5))^{2}+(4-2)^{2}}\\=\sqrt{(-3+5)^{2}+(2)^{2}}\\=\sqrt{(2)^{2}+(2)^{2}}\\=\sqrt{4+4}\\=\sqrt{8}\)

BC = \(\sqrt{(1-(-3))^{2}+(0-4)^{2}}\\=\sqrt{(1+3)^{2}+(-4)^{2}}\\=\sqrt{(4)^{2}+(-4)^{2}}\\=\sqrt{16+16}\\=\sqrt{32}\)

CD = \(\sqrt{(-1-1)^{2}+(-2-0)^{2}}\\=\sqrt{(-2)^{2}+(-2)^{2}}\\=\sqrt{4+4}\\=\sqrt{8}\)

AD = \(\sqrt{(-1-(-5))^{2}+(-2-2)^{2}}\\=\sqrt{(-1+5)^{2}+(-4)}\\=\sqrt{(4)^{2}+(-4)^{2}}\\=\sqrt{16+16}\\=\sqrt{32}\)

Here, AB = CD and AD = BC.

Slope of AB = (y₂ - y₁)/ (x₂ - x₁) = (4 - 2)/ (-3 + 5) = 2/2 = 1

Slope of CD = (-2 - 0)/ (-1 - 1) = -2/-2 = 1

Therefore, the given coordinate points represent a rectangle.

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The following set of coordinates represents which figure? (-5 ,2), (-3, 4), (1, 0), (-1, -2)

Summary:

The following set of coordinates (-5 ,2), (-3, 4), (1, 0), (-1, -2) represents a rectangle.