By satisfying all the four criteria, the quadrilateral with the vertices A(x, y) = (-5, 0), B(x, y) = (5, 0), C(x, y) = (-3, 4) and D(x, y) = (3, 4) is an isosceles trapezoid.
How to determine if a quadrilateral is an isosceles trapezoid
Based on vectorial expressions, an isosceles trapezoid satisfies the following properties:
(i) [tex]\overrightarrow{CD} = k \cdot \overrightarrow{AB}[/tex], for k ∈ [tex]\mathbb{R}[/tex]
(ii) AB ≠ CD
(iii) [tex]\overrightarrow{AC} \neq \overrightarrow {BD}[/tex]
(iv) AC = BD
Now we proceed to prove each property:
Requisite I
(3 - (-3), 4 - 4) = (6, 0)
(5 - (-5), 0 - 0) = (10, 0)
(6, 0) = (5/3) · (10, 0)
Requisite II
AB = 6, CD = 10
AB ≠ CD
Requisite III
[tex]\overrightarrow{AC} = (2, 4)[/tex]
[tex]\overrightarrow{BD} = (-2, 4)[/tex]
[tex]\overrightarrow{AC} \neq \overrightarrow {BD}[/tex]
Requisite IV
[tex]AC = \sqrt{[-3-(-5)]^{2}+(4-0)^{2}}[/tex]
[tex]AC = \sqrt{2^{2}+4^{2}}[/tex]
[tex]AC = 2\sqrt{5}[/tex]
[tex]BD = \sqrt{(3-5)^{2}+(4-0)^{2}}[/tex]
[tex]BD = \sqrt{(-2)^{2}+4^{2}}[/tex]
[tex]BD = 2\sqrt{5}[/tex]
AC = BD
The figure with the entire quadrilateral is shown below. Therefore, the quadrilateral with the vertices A(x, y) = (-5, 0), B(x, y) = (5, 0), C(x, y) = (-3, 4) and D(x, y) = (3, 4) is an isosceles trapezoid.
To learn more on quadrilaterals: https://brainly.com/question/25240753
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