If there is one prayer that you should pray/sing every day and every hour, it is the
LORD's prayer (Our FATHER in Heaven prayer)
 Samuel Dominic Chukwuemeka
It is the most powerful prayer.
A pure heart, a clean mind, and a clear conscience is necessary for it.
Glory to God in the highest; and on earth, peace to people on whom His favor rests!
 Luke 2:14
The Joy of a Teacher is the Success of his Students.
 Samuel Dominic Chukwuemeka
Geometry Transformations Calculators
I greet you this day,
You are encouraged to: solve the questions graphically (by construction); verify the solutions algebraically (by formulas); then use the calculators to check your answers.
These topics are covered in my Videos on Geometry Transformations.
I wrote the codes for these calculators using Javascript, a clientside scripting language. Please use the latest Internet browsers. The calculators should work.
At the moment, only the calculators for the Translations, Reflections, and Rotations are completed. Please check back for the remaining ones later.
Comments, ideas, areas of improvement, questions, and constructive criticisms are welcome. You may contact me.
If you are my student, please do not contact me here. Contact me via the school's system.
Thank you for visiting!!!
Samuel Chukwuemeka (Samdom For Peace) B.Eng., A.A.T, M.Ed., M.S
 Translation (Sliding or Gliding)
 For any point, (x_{1}, y_{1});
 A translation vector of <x, y> is the same as the translation rule of (x_{1} + x, y_{1}+y)

Say:
preimage = (x_{1}, y_{1}),
translation vector = <x, y>,
image = (x_{2}, y_{2}); 
then:
x_{2} = x_{1} + x
y_{2} = y_{1} + y
Given: preimage, translation vector
To Find: image
Given: image, translation vector
To Find: preimage
Given: preimage, image
To Find: translation vector
 Reflection (Flipping)

On the xaxis, yvalues are zero.
Reflecting across the xaxis: ycoordinate changes, xcoordinate remains. 
On the yaxis, xvalues are zero.
Reflecting across the yaxis: xcoordinate changes, ycoordinate remains.  Reflecting across the origin: both the xcoordinate and the ycoordinate changes.
 Reflecting across the line: x = k (k is a constant); the xcoordinate changes, ycoordinate remains.
 Reflecting across the line: y = k (k is a constant); the ycoordinate changes, xcoordinate remains.
 Reflecting across the line: y = x; both the xcoordinate and the ycoordinate changes.
 For any point, (x, y);
 Reflection across the xaxis gives (x, y)
 Reflection across the yaxis gives (x, y)
 Reflection across the origin gives (x, y)
 Reflection across the line: y = x gives (y, x)
 Reflection across the line: y = k (k is a constant) gives (x, 2k  y)
 Reflection across the line: x = k (k is a constant) gives (2k  x, y)
Given: preimage, line of reflection
To Find: image
Given: image, line of reflection
To Find: preimage
Given: preimage, image
To Find: line of reflection
 Rotation (Turning)
 A preimage is rotated about the "center of rotation" through an "angle of rotation".
 If the preimage is rotated in a counterclockwise direction, the angle of rotation is positive.
 If the preimage is rotated in a clockwise direction, the angle of rotation is negative.

Given:
the preimage (x, y),
the center of rotation as the origin (0, 0),
an angle of rotation, θ;
the image would be (x^{'}, y^{'})
where:
x^{'} = x cosθ  y sinθ
y^{'} = y cosθ + x sinθ  For counterclockwise rotations, use the positive value of θ
 For clockwise rotations, use the negative value of θ

Given:
the preimage (x_{1}, y_{1}),
the center of rotation as any point (x, y),
an angle of rotation, θ;
the image would be (x_{1}^{'}, y_{1}^{'})
where:
x_{1}^{'} = (cosθ(x_{1}  x)  sinθ(y_{1}  y)) + x
y_{1}^{'} = (cosθ(y_{1}  y) + sinθ(x_{1}  x)) + y