Geometry: Transformations (Middle School) Worksheet

Question 1

Point A is located at (2, 3). Translate point A 4 units right and 2 units down. What are the coordinates of A'?

Accepted Answer

The coordinates of A' are (6, 1). Moving 4 units right adds 4 to the x-coordinate, and moving 2 units down subtracts 2 from the y-coordinate.

Question 2

Triangle ABC has vertices A(1, 1), B(4, 1), and C(2, 3). Translate the triangle 3 units left and 5 units up. List the coordinates of A', B', and C'.

Accepted Answer

The translated coordinates are A'(-2, 6), B'(1, 6), and C'(-1, 8). Subtract 3 from each x-coordinate and add 5 to each y-coordinate.

Question 3

Reflect point P(-3, 5) across the x-axis. What are the coordinates of P'?

Accepted Answer

The coordinates of P' are (-3, -5). A reflection across the x-axis keeps the x-coordinate the same and changes the sign of the y-coordinate.

Question 4

Reflect point Q(6, -2) across the y-axis. What are the coordinates of Q'?

Accepted Answer

The coordinates of Q' are (-6, -2). A reflection across the y-axis changes the sign of the x-coordinate and keeps the y-coordinate the same.

Question 5

A point R is at (4, -7). Rotate R 90 degrees counterclockwise about the origin. What are the coordinates of R'?

Accepted Answer

The coordinates of R' are (7, 4). A 90 degree counterclockwise rotation about the origin follows the rule (x, y) becomes (-y, x).

Question 6

A point S is at (-2, 8). Rotate S 180 degrees about the origin. What are the coordinates of S'?

Accepted Answer

The coordinates of S' are (2, -8). A 180 degree rotation about the origin changes the sign of both coordinates.

Question 7

Rectangle WXYZ has vertices W(1, 2), X(5, 2), Y(5, 4), and Z(1, 4). Dilate the rectangle by a scale factor of 2 with the center of dilation at the origin. List the coordinates of W', X', Y', and Z'.

Accepted Answer

The dilated coordinates are W'(2, 4), X'(10, 4), Y'(10, 8), and Z'(2, 8). A dilation by a scale factor of 2 from the origin multiplies each coordinate by 2.

Question 8

A triangle has side lengths 3 cm, 4 cm, and 5 cm. It is dilated by a scale factor of 3. What are the side lengths of the new triangle?

Accepted Answer

The new side lengths are 9 cm, 12 cm, and 15 cm. A dilation with scale factor 3 multiplies each side length by 3.

Question 9

Figure A is moved to Figure B by sliding every point 6 units to the right and 1 unit down. What type of transformation is this?

Accepted Answer

This transformation is a translation. A translation slides a figure without turning it, flipping it, or changing its size.

Question 10

A figure is flipped over a line so that each point and its image are the same distance from the line. What type of transformation is this?

Accepted Answer

This transformation is a reflection. A reflection flips a figure across a line called the line of reflection.

Question 11

The rule (x, y) becomes (x + 2, y - 4) is applied to a figure. Describe the transformation in words.

Accepted Answer

The transformation is a translation 2 units right and 4 units down. Adding 2 to x moves the figure right, and subtracting 4 from y moves it down.

Question 12

The rule (x, y) becomes (-x, y) is applied to a figure. Identify the transformation.

Accepted Answer

The transformation is a reflection across the y-axis. The x-coordinate changes sign, and the y-coordinate stays the same.

Question 13

A shape is rotated 90 degrees clockwise about the origin. Point T(-5, 3) is on the shape. What are the coordinates of T'?

Accepted Answer

The coordinates of T' are (3, 5). A 90 degree clockwise rotation about the origin follows the rule (x, y) becomes (y, -x).

Question 14

A quadrilateral has vertices A(-1, 2), B(2, 2), C(3, -1), and D(-2, -1). Reflect the quadrilateral across the x-axis. List the coordinates of A', B', C', and D'.

Accepted Answer

The reflected coordinates are A'(-1, -2), B'(2, -2), C'(3, 1), and D'(-2, 1). A reflection across the x-axis changes the sign of each y-coordinate.

Question 15

A figure is transformed using the rule (x, y) becomes (0.5x, 0.5y). Is the image larger, smaller, or the same size as the original? Explain.

Accepted Answer

The image is smaller than the original. The rule is a dilation with scale factor 0.5, so all distances from the origin are half as large.

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Geometry: Transformations (Middle School)

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