Enter Ordered Pair ex. (1,2)

Plot this on the Cartesian Graph:

Determine the abcissa for (3,4)

Abcissa = absolute value of x-value
Perpendicular distance to the y-axis
Abcissa = |3| = 3

Determine the ordinate for (3,4)

Ordinate = absolute value of y-value
Perpendicular distance to the x-axis
Ordinate = |4| = 4

Evaluate the ordered pair (3,4)

We start at the coordinates (0,0)
Since our x coordinate of 3 is positive
We move up on the graph 3 space(s)
Since our y coordinate of 4 is positive
We move right on the graph 4 space(s)

Determine the quadrant for (3,4)

Since 3>0 and 4>0
(3,4) is in Quadrant I

Convert the point (3,4°) 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) = (3,4°)
(rcosθ,rsinθ) = (3cos(4),3sin(4))
(rcosθ,rsinθ) = (3(0.99756405026539),3(0.069756473664546))
(rcosθ,rsinθ) = (2.9927,0.2093)
(3,4°) = (2.9927,0.2093)

Determine the quadrant for (2.9927,0.2093)

Since 2.9927>0 and 0.2093>0
(2.9927,0.2093) is in Quadrant I

Convert (3,4) to polar

Cartesian Coordinates are denoted as (x,y)
Polar Coordinates are denoted as (r,θ)
(x,y) = (3,4)

Transform r:

r = ±√x2 + y2
r = ±√32 + 42
r = ±√9 + 16
r = ±√25
r = ±5

Transform θ

θ = tan-1(y/x)
θ = tan-1(4/3)
θ = tan-1(1.3333333333333)
θradians = 0.92729521800161

Convert our angle to degrees

Angle in Degrees  =  Angle in Radians * 180
  π

θdegrees  =  0.92729521800161 * 180
  π

θdegrees  =  166.91313924029
  π

θdegrees = 53.13°
Therefore, (3,4) = (5,53.13°)

Determine the quadrant for (3,4)

Since 3>0 and 4>0
(3,4) is in Quadrant I

Show equivalent coordinates

We add 360°
(3,4° + 360°)
(3,364°)

(3,4° + 360°)
(3,724°)

(3,4° + 360°)
(3,1084°)

Method 2: -(r) + 180°

(-1 * 3,4° + 180°)
(-3,184°)

Method 3: -(r) - 180°

(-1 * 3,4° - 180°)
(-3,-176°)

Determine symmetric point

If (x,y) is symmetric to the origin:
then the point (-x,-y) is also on the graph
(-3, -4)

Determine symmetric point

If (x,y) is symmetric to the x-axis:
then the point (x, -y) is also on the graph
(3, -4)

Determine symmetric point

If (x,y) is symmetric to the y-axis:
then the point (-x, y) is also on the graph
(-3, 4)

Take (3, 4) and rotate 90 degrees
We call this R90°

The formula for rotating a point 90° is:
R90°(x, y) = (-y, x)
R90°(3, 4) = (-(4), 3)
R90°(3, 4) = (-4, 3)

Take (3, 4) and rotate 180 degrees
We call this R180°

The formula for rotating a point 180° is:
R180°(x, y) = (-x, -y)
R180°(3, 4) = (-(3), -(4))
R180°(3, 4) = (-3, -4)

Take (3, 4) and rotate 270 degrees
We call this R270°

The formula for rotating a point 270° is:
R270°(x, y) = (y, -x)
R270°(3, 4) = (4, -(3))
R270°(3, 4) = (4, -3)

Take (3, 4) and reflect over the origin
We call this rorigin

Formula for reflecting over the origin is:
rorigin(x, y) = (-x, -y)
rorigin(3, 4) = (-(3), -(4))
rorigin(3, 4) = (-3, -4)

Take (3, 4) 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(3, 4) = (-(3), 4)
ry-axis(3, 4) = (-3, 4)

Take (3, 4) 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(3, 4) = (3, -(4))
rx-axis(3, 4) = (3, -4)

Final Answer


Abcissa = |3| = 3
Ordinate = |4| = 4
Quadrant = I
Quadrant = I
r = ±5
θradians = 0.92729521800161
(3,4) = (5,53.13°)
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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