Ordered Pair

Plot this on the Cartesian Graph:

Determine the abcissa for (2,3)

Abcissa = absolute value of x-value
Perpendicular distance to the y-axis
Abcissa = |2| = 2

Determine the ordinate for (2,3)

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

Evaluate the ordered pair (2,3)

We start at the coordinates (0,0)
Since our x coordinate of 2 is positive
We move up on the graph 2 space(s)
Since our y coordinate of 3 is positive
We move right on the graph 3 space(s)

Determine the quadrant for (2,3)

Since 2>0 and 3>0
(2,3) is in Quadrant I

Convert the point (2,3°) 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) = (2,3°)
(rcosθ,rsinθ) = (2cos(3),2sin(3))
(rcosθ,rsinθ) = (2(0.99862953475771),2(0.052335956183196))
(rcosθ,rsinθ) = (1.9973,0.1047)
(2,3°) = (1.9973,0.1047)

Determine the quadrant for (1.9973,0.1047)

Since 1.9973>0 and 0.1047>0
(1.9973,0.1047) is in Quadrant I

Convert (2,3) to polar

Cartesian Coordinates are denoted as (x,y)
Polar Coordinates are denoted as (r,θ)
(x,y) = (2,3)

Transform r:

r = ±√x² + y²
r = ±√2² + 3²
r = ±√4 + 9
r = ±√13
r = ±3.605551275464

Transform θ

θ = tan^-1(y/x)
θ = tan^-1(3/2)
θ = tan^-1(1.5)
θ_radians = 0.98279372324733

Convert our angle to degrees

Angle in Degrees  =	Angle in Radians * 180
	π

θdegrees  =	0.98279372324733 * 180
	π

θdegrees  =	176.90287018452
	π

θ_degrees = 56.31°
Therefore, (2,3) = (3.605551275464,56.31°)

Determine the quadrant for (2,3)

Since 2>0 and 3>0
(2,3) is in Quadrant I

Show equivalent coordinates

We add 360°
(2,3° + 360°)
(2,363°)

(2,3° + 360°)
(2,723°)

(2,3° + 360°)
(2,1083°)

Method 2: -(r) + 180°

(-1 * 2,3° + 180°)
(-2,183°)

Method 3: -(r) - 180°

(-1 * 2,3° - 180°)
(-2,-177°)

Determine symmetric point

If (x,y) is symmetric to the origin:
then the point (-x,-y) is also on the graph
(-2, -3)

Determine symmetric point

If (x,y) is symmetric to the x-axis:
then the point (x, -y) is also on the graph
(2, -3)

Determine symmetric point

If (x,y) is symmetric to the y-axis:
then the point (-x, y) is also on the graph
(-2, 3)

Take (2, 3) and rotate 90 degrees
We call this R_90°

The formula for rotating a point 90° is:
R_90°(x, y) = (-y, x)
R_90°(2, 3) = (-(3), 2)
R_90°(2, 3) = (-3, 2)

Take (2, 3) and rotate 180 degrees
We call this R_180°

The formula for rotating a point 180° is:
R_180°(x, y) = (-x, -y)
R_180°(2, 3) = (-(2), -(3))
R_180°(2, 3) = (-2, -3)

Take (2, 3) and rotate 270 degrees
We call this R_270°

The formula for rotating a point 270° is:
R_270°(x, y) = (y, -x)
R_270°(2, 3) = (3, -(2))
R_270°(2, 3) = (3, -2)

Take (2, 3) and reflect over the origin
We call this r_origin

Formula for reflecting over the origin is:
r_origin(x, y) = (-x, -y)
r_origin(2, 3) = (-(2), -(3))
r_origin(2, 3) = (-2, -3)

Take (2, 3) and reflect over the y-axis
We call this r_y-axis

Formula for reflecting over the y-axis is:
r_y-axis(x, y) = (-x, y)
r_y-axis(2, 3) = (-(2), 3)
r_y-axis(2, 3) = (-2, 3)

Take (2, 3) and reflect over the x-axis
We call this r_x-axis

Formula for reflecting over the x-axis is:
r_x-axis(x, y) = (x, -y)
r_x-axis(2, 3) = (2, -(3))
r_x-axis(2, 3) = (2, -3)

Final Answer

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