Ordered Pair

Convert the point (1,4) frompolar to Cartesian Convert (1,4) to polar Cartesian Coordinates are denoted as (x,y)Polar Coordinates are denoted as (r,)(x,y) = (1,4) (1,4 + 360)(1,724) (1,4 + 360)(1,1084)

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Plot this on the Cartesian Graph:


Determine the abcissa for (1,4)

Abcissa = absolute value of x-value
Perpendicular distance to the y-axis
Abcissa = |1| = 1

Determine the ordinate for (1,4)

Ordinate = absolute value of y-value
Perpendicular distance to the x-axis
Ordinate = |4| = 4We start at the coordinates (0,0)
Since our x coordinate of 1 is positive
We move up on the graph 1 space(s)
Since our y coordinate of 4 is positive
We move right on the graph 4 space(s)

Determine the quadrant for (1,4)

Since 1>0 and 4>0
(1,4) is in Quadrant I

Convert the point (1,4°) from
polar to Cartesian

The formula for this is below:

Polar Coordinates are (r,θ)
Cartesian Coordinates are (x,y)
Polar to Cartesian Transformation is
(r,θ) → (x,y) = (rcosθ,rsinθ)
(r,θ) = (1,4°)
(rcosθ,rsinθ) = (1cos(4),1sin(4))
(rcosθ,rsinθ) = (1(0.99756405026539),1(0.069756473664546))
(rcosθ,rsinθ) = (0.9976,0.0698)
(1,4°) = (0.9976,0.0698)

Determine the quadrant for (0.9976,0.0698)

Since 0.9976>0 and 0.0698>0
(0.9976,0.0698) is in Quadrant I

Convert (1,4) to polar

Cartesian Coordinates are denoted as (x,y)
Polar Coordinates are denoted as (r,θ)
(x,y) = (1,4)

Transform r:

r = ±√x2 + y2
r = ±√12 + 42
r = ±√1 + 16
r = ±√17
r = ±4.1231056256177

Transform θ

θ = tan-1(y/x)
θ = tan-1(4/1)
θ = tan-1(4)
θradians = 1.325817663668

Convert our angle to degrees

Angle in Degrees  =  Angle in Radians * 180
  π

θdegrees  =  1.325817663668 * 180
  π

θdegrees  =  238.64717946025
  π

θdegrees = 75.96°
Therefore, (1,4) = (4.1231056256177,75.96°)

Determine the quadrant for (1,4)

Since 1>0 and 4>0
(1,4) is in Quadrant I

Show equivalent coordinates

We add 360°
(1,4° + 360°)
(1,364°)

(1,4° + 360°)
(1,724°)

(1,4° + 360°)
(1,1084°)

Method 2: -(r) + 180°

(-1 * 1,4° + 180°)
(-1,184°)

Method 3: -(r) - 180°

(-1 * 1,4° - 180°)
(-1,-176°)If (x,y) is symmetric to the origin:
then the point (-x,-y) is also on the graph
(-1, -4)If (x,y) is symmetric to the x-axis:
then the point (x, -y) is also on the graph
(1, -4)If (x,y) is symmetric to the y-axis:
then the point (-x, y) is also on the graph
(-1, 4)

Take (1, 4) and rotate 90 degrees
We call this R90°

The formula for rotating a point 90° is:
R90°(x, y) = (-y, x)
R90°(1, 4) = (-(4), 1)
R90°(1, 4) = (-4, 1)

Take (1, 4) and rotate 180 degrees
We call this R180°

The formula for rotating a point 180° is:
R180°(x, y) = (-x, -y)
R180°(1, 4) = (-(1), -(4))
R180°(1, 4) = (-1, -4)

Take (1, 4) and rotate 270 degrees
We call this R270°

The formula for rotating a point 270° is:
R270°(x, y) = (y, -x)
R270°(1, 4) = (4, -(1))
R270°(1, 4) = (4, -1)

Take (1, 4) and reflect over the origin
We call this rorigin

Formula for reflecting over the origin is:
rorigin(x, y) = (-x, -y)
rorigin(1, 4) = (-(1), -(4))
rorigin(1, 4) = (-1, -4)

Take (1, 4) and reflect over the y-axis
We call this ry-axis

Formula for reflecting over the y-axis is:
ry-axis(x, y) = (-x, y)
ry-axis(1, 4) = (-(1), 4)
ry-axis(1, 4) = (-1, 4)

Take (1, 4) and reflect over the x-axis
We call this rx-axis

Formula for reflecting over the x-axis is:
rx-axis(x, y) = (x, -y)
rx-axis(1, 4) = (1, -(4))
rx-axis(1, 4) = (1, -4)

Abcissa = |1| = 1
Ordinate = |4| = 4
Quadrant = I
Quadrant = I
r = ±4.1231056256177
θradians = 1.325817663668
(1,4) = (4.1231056256177,75.96°)
Quadrant = I

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How does the Ordered Pair Calculator work?

Free Ordered Pair Calculator - This calculator handles the following conversions:
* Ordered Pair Evaluation and symmetric points including the abcissa and ordinate
* Polar coordinates of (r,θ°) to Cartesian coordinates of (x,y)
* Cartesian coordinates of (x,y) to Polar coordinates of (r,θ°)
* Quadrant (I,II,III,IV) for the point entered.
* Equivalent Coordinates of a polar coordinate
* Rotate point 90°, 180°, or 270°
* reflect point over the x-axis
* reflect point over the y-axis
* reflect point over the origin
This calculator has 1 input.

What 2 formulas are used for the Ordered Pair Calculator?

Cartesian Coordinate = (x, y)
(r,θ) → (x,y) = (rcosθ,rsinθ)

For more math formulas, check out our Formula Dossier

What 15 concepts are covered in the Ordered Pair Calculator?

cartesiana plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in the same unit of lengthcoordinatesA set of values that show an exact positioncoscos(θ) is the ratio of the adjacent side of angle θ to the hypotenusedegreeA unit of angle measurement, or a unit of temperature measurementordered pairA pair of numbers signifying the location of a point
(x, y)pointan exact location in the space, and has no length, width, or thicknesspolara two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference directionquadrant1 of 4 sections on the Cartesian graph. Quadrant I: (x, y), Quadrant II (-x, y), Quadrant III, (-x, -y), Quadrant IV (x, -y)quadrant1 of 4 sections on the Cartesian graph. Quadrant I: (x, y), Quadrant II (-x, y), Quadrant III, (-x, -y), Quadrant IV (x, -y)rectangularA 4-sided flat shape with straight sides where all interior angles are right angles (90°). reflecta flip creating a mirror image of the shaperotatea motion of a certain space that preserves at least one point.sinsin(θ) is the ratio of the opposite side of angle θ to the hypotenusex-axisthe horizontal plane in a Cartesian coordinate systemy-axisthe vertical plane in a Cartesian coordinate system

Example calculations for the Ordered Pair Calculator

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