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?

Answer 1

The answer is below

Explanation:

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

`|AB|=√((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=√((8-5)^2+(8-8)^2) =3\\\\breadth=√((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|=√((5-(-2))^2+(5-5)^2) =7\\\\lenght=|BC|=√((5-5)^2+(-9-5)^2) =14`

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