Distance b/w (1.00, -5.00) & (-8.00, 8.00): Calculate & Polar Coords

  • Thread starter albinoboy
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In summary, the formula for calculating the distance between two points is d = √[(x2 - x1)^2 + (y2 - y1)^2], where (x1, y1) and (x2, y2) are the coordinates of the two points. To find the distance between specific points, we plug in the coordinates into the distance formula. Polar coordinates are a way of representing points in a two-dimensional coordinate system using a radius and an angle. To convert Cartesian coordinates to polar coordinates, we use the formulas r = √(x^2 + y^2) and θ = tan^-1(y/x). The polar coordinate representations of the points (1.00, -5.00
  • #1
albinoboy
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Homework Statement


Two points in the xy plane have Cartesian coordinates (1.00, -5.00) m and (-8.00, 8.00) m.
(a) Determine the distance between these points.
in m

(b) Determine their polar coordinates.
(1.00, -5.00)
r = m
θ = ° (counterclockwise from the + x-axis is positive)

(-8.00, 8.00)
r = m
θ = ° (counterclockwise from the + x-axis is positive)
 
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  • #2
Welcome to PF!

Hi albinoboy! Welcome to PF! :wink:

Show us what you've done, and where you're stuck, and then we'll know how to help! :smile:
 

Related to Distance b/w (1.00, -5.00) & (-8.00, 8.00): Calculate & Polar Coords

1. What is the distance between the two given points?

The distance between the points (1.00, -5.00) and (-8.00, 8.00) is approximately 14.14 units. This can be calculated using the distance formula: d = √[(x2-x1)^2 + (y2-y1)^2], where x1 and y1 are the coordinates of the first point and x2 and y2 are the coordinates of the second point.

2. How do you calculate the distance between two points using coordinates?

The distance between two points can be calculated using the distance formula: d = √[(x2-x1)^2 + (y2-y1)^2], where x1 and y1 are the coordinates of the first point and x2 and y2 are the coordinates of the second point. Simply plug in the values of the coordinates and solve for the distance.

3. Can the distance between two points be negative?

No, the distance between two points cannot be negative. Distance is always a positive value, representing the length between two points.

4. What are polar coordinates and how are they related to calculating distance between two points?

Polar coordinates are a way of representing points in a two-dimensional plane using a distance from the origin and an angle. The distance between two points can be calculated using polar coordinates by finding the difference between the two distances from the origin and the difference between the two angles, and then using the distance formula to find the overall distance.

5. How do you convert Cartesian coordinates to polar coordinates?

To convert Cartesian coordinates (x, y) to polar coordinates (r, θ), use the following formulas: r = √(x^2 + y^2) and θ = arctan(y/x). This will give you the distance from the origin and the angle in radians. Be sure to check the quadrant of the point to determine the correct value of θ.

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