Ordered Pair

Enter Ordered Pair ex. (1,2)

Plot this on the Cartesian Graph:

Determine the abcissa for (2,-6)

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

Determine the ordinate for (2,-6)

Ordinate = absolute value of y-value
Perpendicular distance to the x-axis
Ordinate = |-6| = 6

Evaluate the ordered pair (2,-6)

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 -6 is negative
We move left on the graph 6 space(s)

Determine the quadrant for (2,-6)

Since 2>0 and -6<0
(2,-6) is in Quadrant IV

Convert the point (2,-6°) 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,-6°)
(rcosθ,rsinθ) = (2cos(-6),2sin(-6))
(rcosθ,rsinθ) = (2(0.99452189538078),2(-0.10452846314865))
(rcosθ,rsinθ) = (1.989,-0.2091)
(2,-6°) = (1.989,-0.2091)

Determine the quadrant for (1.989,-0.2091)

Since 1.989>0 and -0.2091<0
(1.989,-0.2091) is in Quadrant IV

Convert (2,-6) to polar

Cartesian Coordinates are denoted as (x,y)
Polar Coordinates are denoted as (r,θ)
(x,y) = (2,-6)

Transform r:

r = ±√x² + y²
r = ±√2² + -6²
r = ±√4 + 36
r = ±√40
r = ±6.3245553203368

Transform θ

θ = tan^-1(y/x)
θ = tan^-1(-6/2)
θ = tan^-1(-3)
θ_radians = -1.2490457723983

Convert our angle to degrees

Angle in Degrees  =	Angle in Radians * 180
	π

θdegrees  =	-1.2490457723983 * 180
	π

θdegrees  =	-224.82823903169
	π

θ_degrees = -71.57°
Therefore, (2,-6) = (6.3245553203368,-71.57°)

Determine the quadrant for (2,-6)

Since 2>0 and -6<0
(2,-6) is in Quadrant IV

Show equivalent coordinates

We add 360°
(2,-6° + 360°)
(2,354°)

(2,-6° + 360°)
(2,714°)

(2,-6° + 360°)
(2,1074°)

Method 2: -(r) + 180°

(-1 * 2,-6° + 180°)
(-2,174°)

Method 3: -(r) - 180°

(-1 * 2,-6° - 180°)
(-2,-186°)

Determine symmetric point

If (x,y) is symmetric to the origin:
then the point (-x,-y) is also on the graph
(-2, 6)

Determine symmetric point

If (x,y) is symmetric to the x-axis:
then the point (x, -y) is also on the graph
(2, 6)

Determine symmetric point

If (x,y) is symmetric to the y-axis:
then the point (-x, y) is also on the graph
(-2, -6)

Take (2, -6) 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, -6) = (-(-6), 2)
R_90°(2, -6) = (6, 2)

Take (2, -6) 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, -6) = (-(2), -(-6))
R_180°(2, -6) = (-2, 6)

Take (2, -6) 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, -6) = (-6, -(2))
R_270°(2, -6) = (-6, -2)

Take (2, -6) 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, -6) = (-(2), -(-6))
r_origin(2, -6) = (-2, 6)

Take (2, -6) 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, -6) = (-(2), -6)
r_y-axis(2, -6) = (-2, -6)

Take (2, -6) 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, -6) = (2, -(-6))
r_x-axis(2, -6) = (2, 6)

Final Answer

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