Plot this on the Cartesian Graph:
Determine the abcissa for (2%2C3,)
Abcissa = absolute value of x-value
Perpendicular distance to the y-axis
Abcissa = |2%2C3| =
2Determine the ordinate for (2%2C3,)
Ordinate = absolute value of y-value
Perpendicular distance to the x-axis
Ordinate = || =
0We start at the coordinates (0,0)
Since our x coordinate of 2%2C3 is positive
We move up on the graph 2 space(s)
Since our y coordinate of is 0
We stay put on the graph 0 space(s)
Determine the quadrant for (2%2C3,)
Since 2%2C3>0 and =0
(2%2C3,) is in Quadrant Between I and IV
Convert the point (2%2C3,°) from
polar to CartesianThe 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%2C3,°)
(rcosθ,rsinθ) = (2%2C3cos(),2%2C3sin())
(rcosθ,rsinθ) = (2%2C3(1),2%2C3(0))
(rcosθ,rsinθ) =
(2,0)(2%2C3,°) =
(2,0)Determine the quadrant for (2,0)
Since 2>0 and 0=0
(2,0) is in Quadrant Between I and IV
Convert
(2%2C3,) to polar Cartesian Coordinates are denoted as (x,y)
Polar Coordinates are denoted as (r,θ)
(x,y) = (2%2C3,)
Transform r:
r = ±√
x2 + y2r = ±√
2%2C32 + 2r = ±√
4 + 0r = ±√
4r =
±2Transform θ
θ = tan
-1(y/x)
θ = tan
-1(/2%2C3)
θ = tan
-1(0)
θ
radians = 0
Convert our angle to degrees
Angle in Degrees = | Angle in Radians * 180 |
| π |
θ
degrees =
0°Therefore, (2%2C3,) =
(2,0°)Determine the quadrant for (2%2C3,)
Since 2%2C3>0 and =0
(2%2C3,) is in Quadrant Between I and IV
Show equivalent coordinates
We add 360°
(2%2C3,° + 360°)
(2%2C3,360°)
(2%2C3,° + 360°)
(2%2C3,720°)
(2%2C3,° + 360°)
(2%2C3,1080°)
Method 2: -(r) + 180°
(-1 * 2%2C3,° + 180°)
(-2,180°)
Method 3: -(r) - 180°
(-1 * 2%2C3,° - 180°)
(-2,-180°)
If (x,y) is symmetric to the origin:
then the point (-x,-y) is also on the graph
(-2, 0)
If (x,y) is symmetric to the x-axis:
then the point (x, -y) is also on the graph
(2%2C3, 0)
If (x,y) is symmetric to the y-axis:
then the point (-x, y) is also on the graph
(-2, )
Take (2%2C3, ) and
rotate 90 degreesWe call this R
90°The formula for rotating a point 90° is:
R
90°(x, y) = (-y, x)
R
90°(2%2C3, ) = (-(), 2%2C3)
R
90°(2%2C3, ) =
(0, 2%2C3)Take (2%2C3, ) and
rotate 180 degreesWe call this R
180°The formula for rotating a point 180° is:
R
180°(x, y) = (-x, -y)
R
180°(2%2C3, ) = (-(2%2C3), -())
R
180°(2%2C3, ) =
(-2, 0)Take (2%2C3, ) and
rotate 270 degreesWe call this R
270°The formula for rotating a point 270° is:
R
270°(x, y) = (y, -x)
R
270°(2%2C3, ) = (, -(2%2C3))
R
270°(2%2C3, ) =
(, -2)Take (2%2C3, ) and
reflect over the originWe call this r
originFormula for reflecting over the origin is:
r
origin(x, y) = (-x, -y)
r
origin(2%2C3, ) = (-(2%2C3), -())
r
origin(2%2C3, ) =
(-2, 0)Take (2%2C3, ) and
reflect over the y-axisWe call this r
y-axisFormula for reflecting over the y-axis is:
r
y-axis(x, y) = (-x, y)
r
y-axis(2%2C3, ) = (-(2%2C3), )
r
y-axis(2%2C3, ) =
(-2, )Take (2%2C3, ) and
reflect over the x-axisWe call this r
x-axisFormula for reflecting over the x-axis is:
r
x-axis(x, y) = (x, -y)
r
x-axis(2%2C3, ) = (2%2C3, -())
r
x-axis(2%2C3, ) =
(2%2C3, 0)Abcissa = |2%2C3| = 2
Ordinate = || = 0
Quadrant = Between I and IV
Quadrant = Between I and IV
r = ±2
θradians = 0
(2%2C3,) = (2,0°)
Quadrant = Between I and 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
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