Enter Ordered Pair ex. (1,2)

Plot this on the Cartesian Graph:

Determine the abcissa for (6,19)

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

Determine the ordinate for (6,19)

Ordinate = absolute value of y-value
Perpendicular distance to the x-axis
Ordinate = |19| = 19

Evaluate the ordered pair (6,19)

We start at the coordinates (0,0)
Since our x coordinate of 6 is positive
We move up on the graph 6 space(s)
Since our y coordinate of 19 is positive
We move right on the graph 19 space(s)

Determine the quadrant for (6,19)

Since 6>0 and 19>0
(6,19) is in Quadrant I

Convert the point (6,19°) 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) = (6,19°)
(rcosθ,rsinθ) = (6cos(19),6sin(19))
(rcosθ,rsinθ) = (6(0.94551857572268),6(0.32556815409888))
(rcosθ,rsinθ) = (5.6731,1.9534)
(6,19°) = (5.6731,1.9534)

Determine the quadrant for (5.6731,1.9534)

Since 5.6731>0 and 1.9534>0
(5.6731,1.9534) is in Quadrant I

Convert (6,19) to polar

Cartesian Coordinates are denoted as (x,y)
Polar Coordinates are denoted as (r,θ)
(x,y) = (6,19)

Transform r:

r = ±√x2 + y2
r = ±√62 + 192
r = ±√36 + 361
r = ±√397
r = ±19.924858845171

Transform θ

θ = tan-1(y/x)
θ = tan-1(19/6)
θ = tan-1(3.1666666666667)
θradians = 1.26491745539

Convert our angle to degrees

Angle in Degrees  =  Angle in Radians * 180
  π

θdegrees  =  1.26491745539 * 180
  π

θdegrees  =  227.68514197021
  π

θdegrees = 72.47°
Therefore, (6,19) = (19.924858845171,72.47°)

Determine the quadrant for (6,19)

Since 6>0 and 19>0
(6,19) is in Quadrant I

Show equivalent coordinates

We add 360°
(6,19° + 360°)
(6,379°)

(6,19° + 360°)
(6,739°)

(6,19° + 360°)
(6,1099°)

Method 2: -(r) + 180°

(-1 * 6,19° + 180°)
(-6,199°)

Method 3: -(r) - 180°

(-1 * 6,19° - 180°)
(-6,-161°)

Determine symmetric point

If (x,y) is symmetric to the origin:
then the point (-x,-y) is also on the graph
(-6, -19)

Determine symmetric point

If (x,y) is symmetric to the x-axis:
then the point (x, -y) is also on the graph
(6, -19)

Determine symmetric point

If (x,y) is symmetric to the y-axis:
then the point (-x, y) is also on the graph
(-6, 19)

Take (6, 19) and rotate 90 degrees
We call this R90°

The formula for rotating a point 90° is:
R90°(x, y) = (-y, x)
R90°(6, 19) = (-(19), 6)
R90°(6, 19) = (-19, 6)

Take (6, 19) and rotate 180 degrees
We call this R180°

The formula for rotating a point 180° is:
R180°(x, y) = (-x, -y)
R180°(6, 19) = (-(6), -(19))
R180°(6, 19) = (-6, -19)

Take (6, 19) and rotate 270 degrees
We call this R270°

The formula for rotating a point 270° is:
R270°(x, y) = (y, -x)
R270°(6, 19) = (19, -(6))
R270°(6, 19) = (19, -6)

Take (6, 19) and reflect over the origin
We call this rorigin

Formula for reflecting over the origin is:
rorigin(x, y) = (-x, -y)
rorigin(6, 19) = (-(6), -(19))
rorigin(6, 19) = (-6, -19)

Take (6, 19) 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(6, 19) = (-(6), 19)
ry-axis(6, 19) = (-6, 19)

Take (6, 19) 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(6, 19) = (6, -(19))
rx-axis(6, 19) = (6, -19)

Final Answer


Abcissa = |6| = 6
Ordinate = |19| = 19
Quadrant = I
Quadrant = I
r = ±19.924858845171
θradians = 1.26491745539
(6,19) = (19.924858845171,72.47°)
Quadrant = I


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Common Core State Standards In This Lesson
CCSS.MATH.CONTENT.6.NS.C.6.B
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)
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

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