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)
It is the most powerful prayer. A pure heart, a clean mind, and a clear conscience is necessary for it.
- Samuel Dominic Chukwuemeka

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 client-side 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, (x1, y1);
• A translation vector of <x, y> is the same as the translation rule of (x1 + x, y1+y)
• Say:
preimage = (x1, y1),
translation vector = <x, y>,
image = (x2, y2);
• then:
x2 = x1 + x
y2 = y1 + y

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To Find: translation vector

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• Reflection (Flipping)
• On the x-axis, y-values are zero.
Reflecting across the x-axis: y-coordinate changes, x-coordinate remains.
• On the y-axis, x-values are zero.
Reflecting across the y-axis: x-coordinate changes, y-coordinate remains.
• Reflecting across the origin: both the x-coordinate and the y-coordinate changes.
• Reflecting across the line: x = k (k is a constant); the x-coordinate changes, y-coordinate remains.
• Reflecting across the line: y = k (k is a constant); the y-coordinate changes, x-coordinate remains.
• Reflecting across the line: y = x; both the x-coordinate and the y-coordinate changes.
• For any point, (x, y);
• Reflection across the x-axis gives (x, -y)
• Reflection across the y-axis 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)

To Find: image

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reflect across the:

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To Find: preimage

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reflected across the:

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To Find: line of reflection

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• 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 (x1, y1),
the center of rotation as any point (x, y),
an angle of rotation, θ;
the image would be (x1', y1')
where:
x1' = (cosθ(x1 - x) - sinθ(y1 - y)) + x
y1' = (cosθ(y1 - y) + sinθ(x1 - x)) + y

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