Transformations on a Grid

Question 1

A point of a shape is at (1, 2). The shape is translated 3 units right and 2 units up. What are the coordinates of that point after the translation?

Accepted Answer

(4, 4)

Answer

(−2, 0)

Answer

(4, 0)

Answer

(1, 2)

Question 2

A square has corners at A(1,2), B(4,2), C(4,5) and D(1,5) on a grid. It is reflected across the vertical line x = 3. Which statement best explains why the reflected square is congruent to the original?

Accepted Answer

A reflection only flips the shape; it never stretches or shrinks, so all side lengths and angles remain unchanged.

Answer

The reflection changes each x‑coordinate by the same amount, so all distances between points stay the same.

Answer

The reflected square has exactly the same list of coordinates as the original, so it must be congruent.

Answer

Because the line x = 3 passes through the center of the square, the image overlaps the original, making them congruent.

Question 3

A triangle has vertices A(1, 3), B(4, 2) and C(3, 5). It is reflected across the vertical line x = 2. What are the coordinates of the reflected triangle’s vertices?

Accepted Answer

A'(3, 3), B'(0, 2), C'(1, 5)

Answer

A'(1, 3), B'(4, 2), C'(3, 5)

Answer

A'(3, 3), B'(0, 2), C'(-1, 5)

Answer

A'(3, 3), B'(0, 2), C'(1, ‑5)

Try three questions

A point of a shape is at (1, 2). The shape is translated 3 units right and 2 units up. What are the coordinates of that point after the translation?

A square has corners at A(1,2), B(4,2), C(4,5) and D(1,5) on a grid. It is reflected across the vertical line x = 3. Which statement best explains why the reflected square is congruent to the original?

A triangle has vertices A(1, 3), B(4, 2) and C(3, 5). It is reflected across the vertical line x = 2. What are the coordinates of the reflected triangle’s vertices?

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