Table of Contents
Why is it not possible to have a negative distance?
It is impossible to have a negative distance. Since it is a scalar quantity, not vector, no matter which way you move you’d be adding to distance. There is no set distance to the point of displacement.
Can a polar coordinates be negative?
In the polar coordinate system, the ordered pair will now be (r, θ). The ordered pair specifies a point’s location based on the value of r and the angle, θ, from the polar axis. The value of r can be positive, negative, or zero. The absolute value of r, |r|, is the distance between the point and the pole.
Can total distance traveled be negative?
Distance traveled is the total length of the path traveled between two positions. Distance traveled is not a vector. It has no direction and, thus, no negative sign.
Is distance positive or negative?
The word distance means how far the object moves regardless of direction. It is always positive and is equal to the absolute value, or magnitude, of the displacement.
How do you know if polar coordinates are positive or negative?
The directed distance, r, is measured from the pole to point P. If point P is on the terminal side of angle θ, then the value of r is positive. If point P is on the opposite side of the pole, then the value of r is negative. The polar coordinates of a point can be written as an ordered pair ( r, θ).
What do negative polar coordinates mean?
When the radius is negative: When graphing a polar coordinate with a negative radius, you move from the pole in the direction opposite the given positive angle (on the same line as the given angle but in the direction opposite to the angle from the pole).
What is the distance between two coordinates?
1. Distance between two points P(x1,y1) and Q(x2,y2) is given by: d(P, Q) = √ (x2 − x1)2 + (y2 − y1)2 {Distance formula} 2. Distance of a point P(x, y) from the origin is given by d(0,P) = √ x2 + y2.
How do you find negative angles in polar coordinates?
Polar Coordinates. If the angle is measured in a clockwise direction, the angle is negative. The directed distance, r, is measured from the pole to point P. If point P is on the terminal side of angle θ, then the value of r is positive. If point P is on the opposite side of the pole, then the value of r is negative.
Can the value of $R$ be negative in polar coordinates?
Polar coordinates are usually defined such that every point $(x,y)$ in $\\mathbb{R}^2$ can be reassigned some value $r\\geq 0$ and $0 \\leq \heta < 2\\pi$. In this formulation, $r$ is a distance. It cannot be negative. It’s the variation of $\heta$ that moves you into different quadrants, not $r$.
How do you find the polar coordinates of a 60 degree Ray?
Consider that the polar coordinates (3,60°) are plotted as a point 3 units from the pole on the 60° ray. The coordinates (−3,240°) will also be plotted exactly at this point because the negative radial distance is measured as a positive distance on the opposite ray (240° − 180° = 60°).
How do you find the ordered pair of polar coordinates?
Polar Coordinates. The directed distance, r, is measured from the pole to point P. If point P is on the terminal side of angle θ, then the value of r is positive. If point P is on the opposite side of the pole, then the value of r is negative. The polar coordinates of a point can be written as an ordered pair ( r, θ).