# Coordinate System Homework: Find Distance and Polar Coords

• chocolatelover
In summary, the bug is located at (1.8, 0.8) m from the origin in a two-dimensional Cartesian coordinate system. It is approximately 1.2 m from the corner of the room. In polar coordinates, its location can be described as having a radius of 1.3 m and an angle of approximately 26.6 degrees from the origin. The two questions are not asking for the same thing, as polar coordinates include both a radius and an angle from the origin. The Pythagorean theorem can be used to calculate the distance in the Cartesian system.
chocolatelover

## Homework Statement

A bug is on one wall of a room. The lower left-hand corner of the wall is selected as the origin of a two-dimensional Cartesian coordinate system. The bug is located at the point having coordinates (1.8, .8) m

How far is it from the corner of the room?
What is it's location in polar coordinates?

r=?
theta=?

## The Attempt at a Solution

Aren't these two question asking for the same thing? I need to use the pythagorean theorem right?

Thank you very much

Last edited:
The radius in the polar system is the distance - it also has a direction

Thank you very much

That makes sense, but aren't these two questions asking for the same thing?

Thank you

Last edited:
No, polar coordinates have both an angle and radius from origin.

Thank you very much

Regards

## 1. What is a coordinate system?

A coordinate system is a system of numbers or coordinates used to uniquely determine the position of a point or object in space. It is used to measure distances, angles, and locations of objects.

## 2. What is the difference between Cartesian and polar coordinates?

Cartesian coordinates, also known as rectangular coordinates, use perpendicular axes (x and y) to locate points in a coordinate plane. Polar coordinates, on the other hand, use a distance (r) from the origin and an angle (θ) to locate points in a coordinate plane.

## 3. How do you find the distance between two points using Cartesian coordinates?

The distance between two points using Cartesian coordinates can be found using the Pythagorean theorem: d = √(x2-x1)^2 + (y2-y1)^2, where (x1, y1) and (x2, y2) are the coordinates of the two points.

## 4. How do you find polar coordinates using Cartesian coordinates?

To find polar coordinates from Cartesian coordinates, you can use the formulas r = √(x^2 + y^2) and θ = tan^-1(y/x). This will give you the distance from the origin and the angle from the positive x-axis, respectively.

## 5. How do you convert between rectangular and polar coordinates?

To convert from rectangular coordinates (x, y) to polar coordinates (r, θ), use the formulas r = √(x^2 + y^2) and θ = tan^-1(y/x). To convert from polar coordinates to rectangular coordinates, use the equations x = r cos(θ) and y = r sin(θ).

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