Enter Ordered Pair


  

Plot this on the Cartesian Graph:


Determine the abcissa for (2,-6)

Abcissa = absolute value of x-value
Perpendicular distance to the y-axis
Abcissa = |2| = 2

Determine the ordinate for (2,-6)

Ordinate = absolute value of y-value
Perpendicular distance to the x-axis
Ordinate = |-6| = 6

Evaluate the ordered pair (2,-6)

We start at the coordinates (0,0)
Since our x coordinate of 2 is positive
We move up on the graph 2 space(s)
Since our y coordinate of -6 is negative
We move left on the graph 6 space(s)

Determine the quadrant for (2,-6)

Since 2>0 and -6<0
(2,-6) is in Quadrant IV

Convert the point (2,-6°) 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) = (2,-6°)
(rcosθ,rsinθ) = (2cos(-6),2sin(-6))
(rcosθ,rsinθ) = (2(0.99452189538078),2(-0.10452846314865))
(rcosθ,rsinθ) = (1.989,-0.2091)
(2,-6°) = (1.989,-0.2091)

Determine the quadrant for (1.989,-0.2091)

Since 1.989>0 and -0.2091<0
(1.989,-0.2091) is in Quadrant IV

Convert (2,-6) to polar

Cartesian Coordinates are denoted as (x,y)
Polar Coordinates are denoted as (r,θ)
(x,y) = (2,-6)

Transform r:

r = ±√x2 + y2
r = ±√22 + -62
r = ±√4 + 36
r = ±√40
r = ±6.3245553203368

Transform θ

θ = tan-1(y/x)
θ = tan-1(-6/2)
θ = tan-1(-3)
θradians = -1.2490457723983

Convert our angle to degrees

Angle in Degrees  =  Angle in Radians * 180
  π

θdegrees  =  -1.2490457723983 * 180
  π

θdegrees  =  -224.82823903169
  π

θdegrees = -71.57°
Therefore, (2,-6) = (6.3245553203368,-71.57°)

Determine the quadrant for (2,-6)

Since 2>0 and -6<0
(2,-6) is in Quadrant IV

Show equivalent coordinates

We add 360°
(2,-6° + 360°)
(2,354°)

(2,-6° + 360°)
(2,714°)

(2,-6° + 360°)
(2,1074°)

Method 2: -(r) + 180°

(-1 * 2,-6° + 180°)
(-2,174°)

Method 3: -(r) - 180°

(-1 * 2,-6° - 180°)
(-2,-186°)

Determine symmetric point

If (x,y) is symmetric to the origin:
then the point (-x,-y) is also on the graph
(-2, 6)

Determine symmetric point

If (x,y) is symmetric to the x-axis:
then the point (x, -y) is also on the graph
(2, 6)

Determine symmetric point

If (x,y) is symmetric to the y-axis:
then the point (-x, y) is also on the graph
(-2, -6)

Take (2, -6) and rotate 90 degrees
We call this R90°

The formula for rotating a point 90° is:
R90°(x, y) = (-y, x)
R90°(2, -6) = (-(-6), 2)
R90°(2, -6) = (6, 2)

Take (2, -6) and rotate 180 degrees
We call this R180°

The formula for rotating a point 180° is:
R180°(x, y) = (-x, -y)
R180°(2, -6) = (-(2), -(-6))
R180°(2, -6) = (-2, 6)

Take (2, -6) and rotate 270 degrees
We call this R270°

The formula for rotating a point 270° is:
R270°(x, y) = (y, -x)
R270°(2, -6) = (-6, -(2))
R270°(2, -6) = (-6, -2)

Take (2, -6) and reflect over the origin
We call this rorigin

Formula for reflecting over the origin is:
rorigin(x, y) = (-x, -y)
rorigin(2, -6) = (-(2), -(-6))
rorigin(2, -6) = (-2, 6)

Take (2, -6) 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(2, -6) = (-(2), -6)
ry-axis(2, -6) = (-2, -6)

Take (2, -6) 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(2, -6) = (2, -(-6))
rx-axis(2, -6) = (2, 6)

Abcissa = |2| = 2
Ordinate = |-6| = 6
Quadrant = IV
Quadrant = IV
r = ±6.3245553203368
θradians = -1.2490457723983
(2,-6) = (6.3245553203368,-71.57°)
Quadrant = IV


You have 2 free calculationss remaining



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?

cartesian
a 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 length
coordinates
A set of values that show an exact position
cos
cos(θ) is the ratio of the adjacent side of angle θ to the hypotenuse
degree
A unit of angle measurement, or a unit of temperature measurement
ordered pair
A pair of numbers signifying the location of a point
(x, y)
point
an exact location in the space, and has no length, width, or thickness
polar
a 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 direction
quadrant
1 of 4 sections on the Cartesian graph. Quadrant I: (x, y), Quadrant II (-x, y), Quadrant III, (-x, -y), Quadrant IV (x, -y)
quadrant
1 of 4 sections on the Cartesian graph. Quadrant I: (x, y), Quadrant II (-x, y), Quadrant III, (-x, -y), Quadrant IV (x, -y)
rectangular
A 4-sided flat shape with straight sides where all interior angles are right angles (90°).
reflect
a flip creating a mirror image of the shape
rotate
a motion of a certain space that preserves at least one point.
sin
sin(θ) is the ratio of the opposite side of angle θ to the hypotenuse
x-axis
the horizontal plane in a Cartesian coordinate system
y-axis
the vertical plane in a Cartesian coordinate system
Example calculations for the Ordered Pair Calculator
  1. (1,4)
  2. (2,3) to polar
  3. (5,30) to Cartesian

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