Question

who moved my triangle?
you and your friend are working on a digital art project. you draw a triangle on the screen, but when you step away for a second, your friend clicks a few buttons and moves it.
now the triangle is in a totally different spot—but its still the same size and shape. you ask your friend what they did, and they say:
i just flipped it, slid it, and spun it a little—nothing major.
you wonder:
wait... in what order did that happen? and how can i tell?
questions:

1. what do you notice about how the triangle changed its position and direction?
2. how could you figure out the exact moves your friend used to transform the shape?

Explanation:

1. Translation (sliding): Moves the triangle without rotating or flipping. Changes position but not orientation.
2. Reflection (flipping): Flips the triangle over a line (like a mirror), reversing its orientation.
3. Rotation (spinning): Turns the triangle around a point by a certain angle.

To determine the order:

• If there’s a reflection, check for flipped orientation.
• Rotation changes the angle of the triangle’s sides.
• Translation just shifts the position.

Answer:

1. The triangle likely underwent translation (slid), reflection (flipped), and rotation (spun). Translation changes position, reflection flips orientation, rotation turns it.
2. Analyze:

• Translation: Check if all points moved the same distance/ direction.
• Reflection: Look for a mirror - like flip (e.g., left - right reversal).
• Rotation: Measure angles of sides before and after. Use coordinate changes (if coordinates are given) to calculate each transformation’s parameters (e.g., reflection line, rotation center/angle, translation vector).