Review the key concepts, formulae, and examples before starting your quiz.
🔑Concepts
Transformation: A general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure.
Translation: Moving a shape without rotating or flipping it. The shape looks exactly the same, just in a different place (sliding).
Reflection: A transformation that acts like a mirror. Every point is the same distance from the central line (mirror line) as the original shape.
Mirror Line (Axis of Reflection): The fixed line across which a figure is reflected. It can be horizontal, vertical, or diagonal.
Congruence: In both reflections and translations, the image remains 'congruent' to the original, meaning it has the same size and shape.
Object and Image: The original shape is called the 'Object', and the shape after the transformation is called the 'Image'.
📐Formulae
Translation Rule: where is the horizontal shift and is the vertical shift.
Reflection over the x-axis:
Reflection over the y-axis:
💡Examples
Problem 1:
A triangle has a vertex at . If the triangle is translated 3 units to the right and 2 units down, what are the new coordinates of ?
Solution:
Explanation:
To move 3 units right, add 3 to the x-coordinate: . To move 2 units down, subtract 2 from the y-coordinate: .
Problem 2:
Reflect the point across the x-axis. What are the coordinates of the image ?
Solution:
Explanation:
When reflecting across the x-axis, the x-coordinate remains the same, but the y-coordinate changes its sign (multiplied by -1).
Problem 3:
A square is reflected across a vertical mirror line . If a vertex of the square is at , what is the x-coordinate of the reflected vertex?
Solution:
Explanation:
The original vertex is 3 units away from the mirror line (). The reflected image must also be 3 units away on the other side: .