Chapter 9.1, Problem 87AYU

Is the street system in your town based on a rectangular coordinate system, a polar coordinate system, or some other system? Explain.

To determine

To explain: Is the street system in your town based on a rectangular coordinate system, a polar coordinate system, or some other system.

Answer to Problem 87AYU

Solution:

We have always used a system of rectangular coordinates to plot points in the plane. Now we are ready to describe another system, called polar coordinates. In many instances, polar coordinates offer certain advantages over rectangular coordinates. In a rectangular coordinate system, you will recall, a point in the plane is represented by an ordered pair of numbers ($x$, $y$), where $x$ and $y$ equal the signed distances of the point from the $y\text{-axis}$ and the $x\text{-axis}$, respectively. In a polar coordinate system, we select a point, called the pole, and then a ray with vertex at the pole, called the polar axis. Comparing the rectangular and polar coordinate systems, note that the origin in rectangular coordinates coincides with the pole in polar coordinates, and the positive $x\text{-axis}$ in rectangular coordinates coincides with the polar axis in polar coordinates.

In plain city we use rectangular coordinate system in street system. But in hill station we use Polar coordinate system in street system.

Explanation of Solution

We have always used a system of rectangular coordinates to plot points in the plane. Now we are ready to describe another system, called polar coordinates. In many instances, polar coordinates offer certain advantages over rectangular coordinates. In a rectangular coordinate system, you will recall, a point in the plane is represented by an ordered pair of numbers ($x$, $y$), where $x$ and $y$ equal the signed distances of the point from the $y\text{-axis}$ and the $x\text{-axis}$, respectively. In a polar coordinate system, we select a point, called the pole, and then a ray with vertex at the pole, called the polar axis. Comparing the rectangular and polar coordinate systems, note that the origin in rectangular coordinates coincides with the pole in polar coordinates, and the positive $x\text{-axis}$ in rectangular coordinates coincides with the polar axis in polar coordinates.

In plain city we use rectangular coordinate system in street system. But in hill station we use Polar coordinate system in street system.