Reflection and Translation on a Grid

Mathematics · Geometry · ages 9-10

Name ______________________ Date ____________

A point slides 3 units right and 2 units up. What happens to its coordinates?
- Add 3 to y and add 2 to x
- Add 3 to x and add 2 to y
- Subtract 3 from x and subtract 2 from y
When you reflect a shape in a vertical mirror line, what happens to the y-coordinate of each point?
- It stays the same
- It changes sign
- It becomes zero
A shape and its reflection are congruent, meaning they are exactly the same size and shape.
Circle one: True False
A shape's corner is at (1, 4). It slides 3 units right and 2 units up. What is its new coordinate?
- (4, 6)
- (4, 2)
- (-2, 6)
Point A is at (2, 5). Reflect it in the vertical line x = 0 (the y-axis). What is the new coordinate?
- (2, -5)
- (-2, -5)
- (-2, 5)
Which of these stays true after you translate a shape across the grid?
- The shape becomes a different size
- The shape stays exactly the same size and shape
- The shape's angles change
A shape's corner moves from (-2, 3) to (1, 0) after a translation. How many units did it move down?
Answer: ______________
Ben reflects a square in a vertical mirror line and says the new square is bigger because it moved further from the mirror line. Is he correct?
- No, reflecting only changes position, never size
- Yes, points further from the mirror line get bigger
- Only if the square starts on the mirror line

Answer key

For grown-ups. Fold this page away before handing over the rest.

Add 3 to x and add 2 to y · Right and up are both increases, so you add to the x-coordinate for right and to the y-coordinate for up.
It stays the same · A vertical mirror line flips left and right, so only the x-coordinate changes. The y-coordinate never moves.
True · A reflection only flips a shape's position. It never changes the size or the angles.
(4, 6) · Add 3 to the x-coordinate for the move right and 2 to the y-coordinate for the move up: (1 + 3, 4 + 2) = (4, 6).
(-2, 5) · The mirror line is vertical, so the x-coordinate flips sign and the y-coordinate stays the same.
The shape stays exactly the same size and shape · Sliding a shape only moves it. It never stretches, shrinks, or bends the shape.
3 · The y-coordinate went from 3 to 0, a drop of 3 units, even though the x-coordinate also changed.
No, reflecting only changes position, never size · Distance from the mirror line changes where a point lands, not its size. Every reflected shape stays congruent to the original.