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Geometry Transformations Practice

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Geometry Transformations Practice

A designer is creating a repeating tile pattern. Solve each task using coordinates, transformation rules and clear mathematical reasoning. Unless stated otherwise, rotations are about the origin (0, 0).

Identify and interpret

Use transformation vocabulary precisely. Remember that a translation, reflection or rotation is an isometry: it preserves lengths and angles.

1.A logo is moved 6 units left and 2 units down without turning or flipping. Name the transformation and give its vector.

2.A point A(-4, 3) is reflected in the y-axis. Which coordinates does A' have?

(4, 3)
(-4, -3)
(4, -3)
(-3, 4)

3.Under a 90° clockwise rotation about the origin, point B(2, -5) maps to B'. Find the coordinates of B'.

4.True or false: A reflection preserves the size and angle measures of a shape, but reverses its orientation.

TrueFalse

Work with coordinates

For coordinate transformations, apply the same rule to every vertex. Keep track of the order when more than one transformation is used.

5.Triangle PQR has vertices P(1, 1), Q(4, 1) and R(2, 3). It is translated by vector (3, -2). Give the coordinates of P', Q' and R'.

6.Point C(-3, 6) is reflected in the x-axis, then translated 4 units right. Find its final coordinates.

7.A point (x, y) is rotated 180° about the origin. Complete the rule: (x, y) → (, ). Then use it to find the image of D(5, -2).

8.A triangle has vertices A(1, 2), B(3, 2) and C(2, 4). Reflect it in the line y = x. State the coordinates of A', B' and C'.

9.A point E(2, 1) is rotated 90° anticlockwise about the origin, then translated by vector (1, 4). Find its final coordinates. Show the intermediate point.

10.Mere says, “If I reflect a shape in the y-axis and then reflect it in the x-axis, that is equivalent to a 180° rotation about the origin.” Is Mere correct? Justify your answer using a general point (x, y).

11.A motif must move from M(2, 1) to M'(-1, 4) by a translation. Write the translation vector and describe the movement in words.

12.For a repeating tile, choose a starting point (2, 1). Apply these transformations in order: reflect in the y-axis, then rotate 90° clockwise about the origin. What is the final image of the point?