Geometry: Transformations (High School) Worksheet

Question 1

Triangle ABC has vertices A(2, 1), B(5, 1), and C(3, 4). Translate the triangle by the vector < -3, 2 >. Give the coordinates of A', B', and C'.

Accepted Answer

The translated coordinates are A'(-1, 3), B'(2, 3), and C'(0, 6). Each original point moves 3 units left and 2 units up.

Question 2

Point P(-4, 7) is reflected across the x-axis. What are the coordinates of P'?

Accepted Answer

The coordinates of P' are (-4, -7). A reflection across the x-axis keeps the x-coordinate the same and changes the sign of the y-coordinate.

Question 3

Point Q(6, -2) is reflected 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 4

Point R(3, -5) is rotated 90 degrees counterclockwise about the origin. What are the coordinates of R'?

Accepted Answer

The coordinates of R' are (5, 3). A 90 degree counterclockwise rotation about the origin maps (x, y) to (-y, x).

Question 5

Point S(-2, 8) is rotated 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 maps (x, y) to (-x, -y).

Question 6

Triangle DEF has vertices D(1, 2), E(4, 2), and F(2, 6). Dilate the triangle by a scale factor of 3 centered at the origin. Give the coordinates of D', E', and F'.

Accepted Answer

The dilated coordinates are D'(3, 6), E'(12, 6), and F'(6, 18). A dilation centered at the origin with scale factor 3 multiplies each coordinate by 3.

Question 7

Rectangle WXYZ has vertices W(-1, 1), X(3, 1), Y(3, 4), and Z(-1, 4). Reflect the rectangle across the line y = x. Give the coordinates of W', X', Y', and Z'.

Accepted Answer

The reflected coordinates are W'(1, -1), X'(1, 3), Y'(4, 3), and Z'(4, -1). A reflection across y = x maps each point (x, y) to (y, x).

Question 8

A transformation maps every point (x, y) to (x + 5, y - 1). Name the transformation and describe it in words.

Accepted Answer

The transformation is a translation. It moves every point 5 units to the right and 1 unit down.

Question 9

A transformation maps every point (x, y) to (-x, y). Name the transformation and identify the line of reflection.

Accepted Answer

The transformation is a reflection across the y-axis. It changes the sign of each x-coordinate while keeping each y-coordinate the same.

Question 10

Point A(2, 3) is first translated by <4, -5> and then reflected across the y-axis. What are the final coordinates of A''?

Accepted Answer

After the translation, A' is (6, -2). Reflecting across the y-axis gives A''(-6, -2).

Question 11

Point B(-3, 4) is reflected across the x-axis and then rotated 90 degrees clockwise about the origin. What are the final coordinates of B''?

Accepted Answer

After reflection across the x-axis, B' is (-3, -4). A 90 degree clockwise rotation maps (x, y) to (y, -x), so B'' is (-4, 3).

Question 12

A triangle has side lengths 5 cm, 7 cm, and 9 cm. It is dilated by a scale factor of 0.5. What are the side lengths of the image triangle, and is the image congruent or similar to the original?

Accepted Answer

The image side lengths are 2.5 cm, 3.5 cm, and 4.5 cm. The image is similar to the original, but it is not congruent because the side lengths changed.

Question 13

Quadrilateral JKLM is rotated 270 degrees counterclockwise about the origin. Which single rotation would produce the same result, and in what direction?

Accepted Answer

A 90 degree clockwise rotation about the origin would produce the same result. Rotating 270 degrees counterclockwise is equivalent to rotating 90 degrees clockwise.

Question 14

Line segment AB has endpoints A(-2, 5) and B(4, 1). It is reflected across the x-axis. Does the length of the segment change? Explain.

Accepted Answer

The length of the segment does not change. A reflection is a rigid motion, so it preserves distances and produces a congruent image.

Question 15

Triangle PQR has vertices P(0, 0), Q(6, 0), and R(2, 4). Triangle P'Q'R' has vertices P'(0, 0), Q'(3, 0), and R'(1, 2). Describe the transformation from triangle PQR to triangle P'Q'R'.

Accepted Answer

The transformation is a dilation centered at the origin with scale factor 1/2. Each coordinate of the original triangle is multiplied by 1/2 to create the image.

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Geometry: Transformations (High School)

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