Plot this on the Cartesian Graph:
Determine the abcissa for (9,8)
Abcissa = absolute value of x-value
Perpendicular distance to the y-axis
Abcissa = |9| =
9Determine the ordinate for (9,8)
Ordinate = absolute value of y-value
Perpendicular distance to the x-axis
Ordinate = |8| =
8We start at the coordinates (0,0)
Since our x coordinate of 9 is positive
We move up on the graph 9 space(s)
Since our y coordinate of 8 is positive
We move right on the graph 8 space(s)
Determine the quadrant for (9,8)
Since 9>0 and 8>0
(9,8) is in Quadrant I
Convert the point (9,8°) 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) = (9,8°)
(rcosθ,rsinθ) = (9cos(8),9sin(8))
(rcosθ,rsinθ) = (9(0.99026806876377),9(0.13917310080207))
(rcosθ,rsinθ) =
(8.9124,1.2526)(9,8°) =
(8.9124,1.2526)Determine the quadrant for (8.9124,1.2526)
Since 8.9124>0 and 1.2526>0
(8.9124,1.2526) is in Quadrant I
Convert
(9,8) to polar Cartesian Coordinates are denoted as (x,y)
Polar Coordinates are denoted as (r,θ)
(x,y) = (9,8)
Transform r:
r = ±√
x2 + y2r = ±√
92 + 82r = ±√
81 + 64r = ±√
145r =
±12.041594578792Transform θ
θ = tan
-1(y/x)
θ = tan
-1(8/9)
θ = tan
-1(0.88888888888889)
θ
radians = 0.72664234068173
Convert our angle to degrees
Angle in Degrees = | Angle in Radians * 180 |
| π |
θdegrees = | 0.72664234068173 * 180 |
| π |
θdegrees = | 130.79562132271 |
| π |
θ
degrees =
41.63°Therefore, (9,8) =
(12.041594578792,41.63°)Determine the quadrant for (9,8)
Since 9>0 and 8>0
(9,8) is in Quadrant I
Show equivalent coordinates
We add 360°
(9,8° + 360°)
(9,368°)
(9,8° + 360°)
(9,728°)
(9,8° + 360°)
(9,1088°)
Method 2: -(r) + 180°
(-1 * 9,8° + 180°)
(-9,188°)
Method 3: -(r) - 180°
(-1 * 9,8° - 180°)
(-9,-172°)
If (x,y) is symmetric to the origin:
then the point (-x,-y) is also on the graph
(-9, -8)
If (x,y) is symmetric to the x-axis:
then the point (x, -y) is also on the graph
(9, -8)
If (x,y) is symmetric to the y-axis:
then the point (-x, y) is also on the graph
(-9, 8)
Take (9, 8) and
rotate 90 degreesWe call this R
90°The formula for rotating a point 90° is:
R
90°(x, y) = (-y, x)
R
90°(9, 8) = (-(8), 9)
R
90°(9, 8) =
(-8, 9)Take (9, 8) and
rotate 180 degreesWe call this R
180°The formula for rotating a point 180° is:
R
180°(x, y) = (-x, -y)
R
180°(9, 8) = (-(9), -(8))
R
180°(9, 8) =
(-9, -8)Take (9, 8) and
rotate 270 degreesWe call this R
270°The formula for rotating a point 270° is:
R
270°(x, y) = (y, -x)
R
270°(9, 8) = (8, -(9))
R
270°(9, 8) =
(8, -9)Take (9, 8) and
reflect over the originWe call this r
originFormula for reflecting over the origin is:
r
origin(x, y) = (-x, -y)
r
origin(9, 8) = (-(9), -(8))
r
origin(9, 8) =
(-9, -8)Take (9, 8) 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(9, 8) = (-(9), 8)
r
y-axis(9, 8) =
(-9, 8)Take (9, 8) 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(9, 8) = (9, -(8))
r
x-axis(9, 8) =
(9, -8)Abcissa = |9| = 9
Ordinate = |8| = 8
Quadrant = I
Quadrant = I
r = ±12.041594578792
θradians = 0.72664234068173
(9,8) = (12.041594578792,41.63°)
Quadrant = I
You have 2 free calculationss remaining
algo = 0
title = Ordered Pair
pl = 1
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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