Online translation quiz: apply (x+a, y+b) to points and shapes

📚 Quick Study Guide

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• Translation Definition: A translation shifts a point or shape without rotating or resizing it. It's like sliding it!
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• Translation Rule: The general rule for translating a point $(x, y)$ is $(x + a, y + b)$, where $a$ determines the horizontal shift and $b$ determines the vertical shift.
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• Horizontal Shift: If $a > 0$, the point shifts to the right. If $a < 0$, it shifts to the left.
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• Vertical Shift: If $b > 0$, the point shifts upwards. If $b < 0$, it shifts downwards.
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• Applying to Shapes: Apply the same translation rule $(x + a, y + b)$ to each vertex (corner point) of the shape.

Practice Quiz

1. What does the transformation $(x+2, y-3)$ do to a point?
   1. Moves it 2 units left and 3 units up.
   2. Moves it 2 units right and 3 units up.
   3. Moves it 2 units left and 3 units down.
   4. Moves it 2 units right and 3 units down.
2. The point (1, 4) is translated by (x-5, y+2). What are the coordinates of the translated point?
   1. (6, 6)
   2. (-4, 6)
   3. (6, 2)
   4. (-4, 2)
3. A triangle has vertices at (0, 0), (1, 0), and (0, 1). If it's translated by (x+3, y+4), what are the new vertices?
   1. (3, 4), (4, 4), (3, 5)
   2. (-3, -4), (-2, -4), (-3, -3)
   3. (4, 3), (5, 3), (4, 2)
   4. (-4, -3), (-5, -3), (-4, -2)
4. If a point is translated by (x+a, y+b) and 'a' is negative, which direction does the point move?
   1. Right
   2. Left
   3. Up
   4. Down
5. A square with vertices (1,1), (2,1), (2,2), (1,2) is translated by (x-1, y-1). What is the new coordinate of the vertex that was originally at (2,2)?
   1. (3,3)
   2. (1,1)
   3. (0,0)
   4. (2,2)
6. What transformation moves the point (5, -2) to (3, 0)?
   1. (x+2, y-2)
   2. (x-2, y+2)
   3. (x+8, y-2)
   4. (x-8, y+2)
7. The point (7, 8) is translated to (7, 2). What is the rule for this translation?
   1. (x, y+6)
   2. (x, y-6)
   3. (x+6, y)
   4. (x-6, y)