In many cities and towns across the United States, the numbering system of the roads is...

In many cities and towns across the United States, the numbering system of the roads is based on a grid, similar to the latitude and longitude lines on a globe. Suppose the green lines in the following graph represent two east-west and two north-south running roads in a Midwestern town.

Write equations for the two horizontal and two vertical lines that represent roads in the town.

2. The Willis Tower (formerly known as the Sears Tower) in Chicago, Illinois, is the tallest building in the United States. Measuring 1,450 feet, the tower contains 110 stories filled with a combination of office and retail space. The base of the tower is made up of nine 75’ × 75’ squares. Suppose the square graphed on the coordinate plane below represents the base of the Willis Tower.

Write equations for the two horizontal and two vertical lines that pass through the square.

3. Think of another real-world situation that might involve horizontal and vertical lines. Write a description of the situation and draw the graph of a coordinate plane with two horizontal and two vertical lines to represent your situation. Draw the lines so that two of them pass through positive values and the other two pass through negative values on the coordinate plane. Then write equations for all four of the lines on your graph.

Solutions

Expert Solution

Q.1 Since no graph is given, it is presumed it may be like the one given below.

Taking center of the town as origin, the vertical line passing through it would be the y axis, like the meridian on the globe and the horizontal line through it would be x axis, like the Equator.

Equation of vertical lines would be x=a or x=b, where 'a' or 'b' is the horizontal distance of the vertical line from y- axis. Equation of horizontal lines would be of the type y=c or d, where 'c' or 'd' is the vertical distance of the horiontal line from x axis.

Let the graph shown below represent the base of Willis Tower, having nine squares of size 75'x75', The horizontal and vertical lines through the center of the square are marked x -axis and y -axis , on either side of the x-axis, would be y= 75 and y = -75 as shown;

The equation of two vertical lines on either side of the y axis, marked in purple pen would be x=75 and x= -75. These lines are also equidistant from origin along x-axis.

A real world situation may be a soccer field. The rectangular field being bounded by two horizontal and two vertical lines. The horizontal line through the center of the filed dividing it into two halves of a coordinate plane is called the center line., One half consisting of positive values (upper half)and the other half (lower) consisting of negative values.

The two vertical lines on either side of a goal post would have equations x=a on the right and x= -a on the left.

The two horizontal lines in front of two goal posts would have equations y=b on the upper side of the center line, and y=-b on the down side of the center line. The middle point of the center line would be the origin and the center line itself would be the x -axis of the coordinate plane. The line perpendicular to the center line,passing through the middle point would be the y -axis of the coordinate plane.

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milcah answered 1 year ago

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