Busby County is rectangular. A map of the county on a coordinate plane shows the vertices of the county at (5, 8), (8, 8),(8,10),and (5,10).

Question

Busby County is rectangular. A map of the county on a coordinate plane shows the vertices of the county at (5, 8), (8, 8),(8,10),and (5,10). What if the coordinates were A(−2, 5), B(5, 5),C(5,−9),and D(−2,−9)? What would the perimeter of the county be?

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Verity 3 years 2021-08-14T19:39:00+00:00 1 Answers 33 views 0

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    2021-08-14T19:40:58+00:00

    Answer:

    The answer is below

    Step-by-step explanation:

    Distance between two points A(x_1,y_1)\ and\ B(x_2,y_2)\ on \ the\ coordinate\ plane

    |AB|=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

    The perimeter of rectangle = 2(length + breadth)

    If the vertices are at (5, 8), (8, 8),(8,10),and (5,10), then:

    length=\sqrt{(8-5)^2+(8-8)^2} =3\\\\breadth=\sqrt{(8-8)^2+(10-8)^2} =2

    The perimeter of the county would be = 2(length + breadth) = 2(3 + 2) = 10 unit

    If the vertices are at A(−2, 5), B(5, 5),C(5,−9),and D(−2,−9), then:

    breadth=|AB|=\sqrt{(5-(-2))^2+(5-5)^2} =7\\\\lenght=|BC|=\sqrt{(5-5)^2+(-9-5)^2} =14

    The perimeter of the county would be = 2(length + breadth) = 2(7 + 14) = 42 unit

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