Plot this on the Cartesian Graph:
Determine the abcissa for (-6,4)
Abcissa = absolute value of x-value
Perpendicular distance to the y-axis
Abcissa = |-6| =
6Determine the ordinate for (-6,4)
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 -6 is negative
We move down on the graph 6 space(s)
Since our y coordinate of 4 is positive
We move right on the graph 4 space(s)
Determine the quadrant for (-6,4)
Since -6<0 and 4>0
(-6,4) is in Quadrant II
Convert the point (-6,4°) 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) = (-6,4°)
(rcosθ,rsinθ) = (-6cos(4),-6sin(4))
(rcosθ,rsinθ) = (-6(0.99756405026539),-6(0.069756473664546))
(rcosθ,rsinθ) =
(-5.9854,-0.4185)(-6,4°) =
(-5.9854,-0.4185)Determine the quadrant for (-5.9854,-0.4185)
Since -5.9854<0 and -0.4185<0
(-5.9854,-0.4185) is in Quadrant III
Convert
(-6,4) to polar Cartesian Coordinates are denoted as (x,y)
Polar Coordinates are denoted as (r,θ)
(x,y) = (-6,4)
Transform r:
r = ±√
x2 + y2r = ±√
-62 + 42r = ±√
36 + 16r = ±√
52r =
±7.211102550928Transform θ
θ = tan
-1(y/x)
θ = tan
-1(4/-6)
θ = tan
-1(-0.66666666666667)
θ
radians = -0.58800260354757
Convert our angle to degrees
Angle in Degrees = | Angle in Radians * 180 |
| π |
θdegrees = | -0.58800260354757 * 180 |
| π |
θdegrees = | -105.84046863856 |
| π |
θ
degrees =
-33.69°Therefore, (-6,4) =
(7.211102550928,-33.69°)Determine the quadrant for (-6,4)
Since -6<0 and 4>0
(-6,4) is in Quadrant II
Show equivalent coordinates
We add 360°
(-6,4° + 360°)
(-6,364°)
(-6,4° + 360°)
(-6,724°)
(-6,4° + 360°)
(-6,1084°)
Method 2: -(r) + 180°
(-1 * -6,4° + 180°)
(6,184°)
Method 3: -(r) - 180°
(-1 * -6,4° - 180°)
(6,-176°)
If (x,y) is symmetric to the origin:
then the point (-x,-y) is also on the graph
(6, -4)
If (x,y) is symmetric to the x-axis:
then the point (x, -y) is also on the graph
(-6, -4)
If (x,y) is symmetric to the y-axis:
then the point (-x, y) is also on the graph
(6, 4)
Take (-6, 4) and
rotate 90 degreesWe call this R
90°The formula for rotating a point 90° is:
R
90°(x, y) = (-y, x)
R
90°(-6, 4) = (-(4), -6)
R
90°(-6, 4) =
(-4, -6)Take (-6, 4) and
rotate 180 degreesWe call this R
180°The formula for rotating a point 180° is:
R
180°(x, y) = (-x, -y)
R
180°(-6, 4) = (-(-6), -(4))
R
180°(-6, 4) =
(6, -4)Take (-6, 4) and
rotate 270 degreesWe call this R
270°The formula for rotating a point 270° is:
R
270°(x, y) = (y, -x)
R
270°(-6, 4) = (4, -(-6))
R
270°(-6, 4) =
(4, 6)Take (-6, 4) and
reflect over the originWe call this r
originFormula for reflecting over the origin is:
r
origin(x, y) = (-x, -y)
r
origin(-6, 4) = (-(-6), -(4))
r
origin(-6, 4) =
(6, -4)Take (-6, 4) 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(-6, 4) = (-(-6), 4)
r
y-axis(-6, 4) =
(6, 4)Take (-6, 4) 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(-6, 4) = (-6, -(4))
r
x-axis(-6, 4) =
(-6, -4)Final Answer
Abcissa = |-6| = 6
Ordinate = |4| = 4
Quadrant = II
Quadrant = III
r = ±7.211102550928
θradians = -0.58800260354757
(-6,4) = (7.211102550928,-33.69°)
Quadrant = II
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)
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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