Write equations for the given roads as follows:
Lewiston Road: y = 2x + 8
Johnson Road: y = -x/2 - 1/2
Chavez Road: y = 2x + 2
Brannon Road: y = -x/2 - 2
Find the intersection of Lewiston and Johnson.
2x + 8 = -x/2 - 1/2
4x + 16 = -x - 1
5x = -17
x = -17/5, y = 2*(-17/5) + 8 = 6/5
Lewiston and Johnson intersect at (-17/5, 6/5)
Find the intersection of Lewiston and Brannon.
2x + 8 = -x/2 - 2
4x + 16 = -x - 4
5x = -20
x = -4, y = 2*(-4) + 8 = 0
Lewiston and Brannon intersect at (-4, 0)
Find the intersection of Johnson and Chavez.
-x/2 - 1/2 = 2x + 2
-x - 1 = 4x + 4
5x = -5
x = -1, y = -2 + 2 = 0
Johnson and Chavez intersect at (-1, 0)
Find the intersection of Chavez and Brannon.
2x + 2 = -x/2 - 2
4x + 4 = -x - 4
5x = -8
x = -8/5, y = 2*(-8/5) + 2 = -6/5
Chavez and Brannon intersect at (-8/5, -6/5)
The quadrilateral that is bounded by the roads is shown in the figure below.
It is a parallelogram ABCD.
AB and CD are parallel and have a slope of -1/2.
BC and AD are parallel and have a slope of 2.
Note:
Because the product of the slopes = -1, AB is perpendicular to AD and BC.
The quadrilateral is actually a rectangle.
Answer:
The boundary defined by the four roads is the rectangle ABCD shown in the figure.
