Figure EFGH on the grid below represents a trapezoidal plate at its starting position on a rotating machine platform: Trapezoid EFGH with vertices E at negative 4 comma 8, F at negative 7 comma 5, G at negative 4 comma 3, and H at negative 2 comma 5. The plate is rotated 720° about the origin in the counterclockwise direction. Which of the following is formed when the arcs of rotation are drawn for each point as it is rotated? They form parallel segments. They form perpendicular segments. They form concentric circles. They form congruent segments.

The correct option is;

They form concentric circles

Step-by-step explanation:

Given that the coordinates of the vertices of the trapezoid are;

E = (-4, 8)

F = (-7, 5)

G = (-4, 3)

H = (-2, 5)

We note that the distances from the origin, O, to the vertices are;

OE = √((-4)² + 8²) = √(80) = 4·√5

OF = √((-7)² + 5²) = √(74)

OG = √((-4)² + 3²) = √(25) = 5

OH = = √((-2)² + 5²) = √(29)

When rotated 720° about the origin, each point behaves as the radius of a circle with center at the origin such that they form concentric circles with OE being the largest circle and OG the smallest circle at the center.

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step-by-step explanation: