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?

The answer is below

Step-by-step explanation:

Distance between two points

The perimeter of rectangle = 2(length + breadth)

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

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:

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

isocolese triangle

we know that the line connect a and b is the hyptonuse

so first find the hypotonuse length using the distance formula, call the length c

since it is an isocolese triangle, the lengths of the legs are the same

using pythagorean theorem,

in this case, a=b since isocolese triangle so we get

or

we can find c so we can find the distances

we know that if we draw 2 circles, each has center at a and b, and find where they intersect, we can the 2 possible locations for c

if a has center at (xa,ya) and b has center at (xb,yb), then we can solve where

and

intersect to find where they intersect

i'm not going to put an example because i have to go to class. i hope this explanation is enough