What is the most precise term for quadrilateral ABCD with vertices A(4, 4), B(5, 8), C(8, 8), and D(8, 5)?

Solution:

Given, ABCD is a quadrilateral.

The vertices are A(4, 4) B(5, 8) C(8, 8), and D(8, 5).

We have to find the most precise term for the quadrilateral ABCD.

Using distance formula,

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

\(AB=\sqrt{(8-4)^{2}+(5-4)^{2}}=\sqrt{16+1}=\sqrt{17}\)

\(BC=\sqrt{(8-8)^{2}+(8-5)^{2}}=\sqrt{0+9}=3\)

\(CD=\sqrt{(8-5)^{2}+(8-8)^{2}}=\sqrt{9+0}=\sqrt{9}=3\)

\(DA=\sqrt{(5-4)^{2}+(8-4)^{2}}=\sqrt{1+16}=\sqrt{17}\)

Since the two disjoint pairs of consecutive sides are congruent as AB = DA and BC = CD

By definition, two disjoint pairs of consecutives sides are congruent,the given quadrilateral is a kite.

Therefore, the given quadrilateral is a kite.

What is the most precise term for quadrilateral ABCD with vertices A(4, 4), B(5, 8), C(8, 8), and D(8, 5)?

Summary:

The most precise term for quadrilateral ABCD with vertices A(4, 4), B(5, 8), C(8, 8), and D(8, 5) is a kite