Worksheet

Tournament Bracket: Score Badge Moves

Use coordinate diagrams and rigid-motion sequences to verify congruent score badges on a youth basketball tournament bracket.

Grade 8MathInteractive · Printable

Aligned to8.G.A.2

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Single worksheet
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1 Common Core standard
Printable answer key
14 questions
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Details

Format: Interactive · Printable
Grade: Grade 8
Subject: Math
Question types: Fill in the blank, Multiple choice, Circle the answer, Short answer

About this worksheet

What students practice

Students identify transformations that preserve the size and shape of tournament graphics.
Students describe sequences of rotations, reflections, and translations linking congruent figures.
Students verify proposed rigid motions using corresponding vertices and side lengths.

How to use

Use after introducing rigid motions. Have students sketch intermediate images on graph paper and check every corresponding vertex before accepting a sequence.

Curriculum

Common Core standard covered

8.G.A.2

Understand congruent figures as ones linked by rotations, reflections, and translations, and describe such a sequence.

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Tournament Bracket: Score Badge Moves

Use rigid motions to check matching graphics on a youth basketball bracket.

Check the Score Badges

The tournament bracket uses geometric badges beside game scores. Congruent badges must match exactly after rigid motions.

Select every edit that guarantees a score badge remains congruent to its original.

Reflect the badge across a vertical line.Double only the badge's width.Rotate the badge 45° about its center.Translate the badge to another game slot.Multiply every side length by 1.5.

The semifinal badge is triangle ABC. A matching badge has corresponding vertices A′(1, −4), B′(1, −2), and C′(4, −4). Which motion maps the shown badge to that copy?

A. Reflect across the x-axis.
B. Rotate 180° about the origin.
C. Rotate 90° clockwise about the origin.
D. Reflect across the line y = x.

A triangular score badge has side lengths 4, 6, and 7 units. It is reflected, rotated, and then translated to the championship slot.

What is the perimeter of the final badge? units

A designer proposes this replacement for a right-triangular score badge. Can rigid motions map the original to the replacement with A → D, B → E, and C → F?

Badge Replacement
Vertex	Original	Replacement
A → D	(−3, −2)	(1, 1)
B → E	(0, −2)	(5, 1)
C → F	(−3, 2)	(1, 4)

A. Yes; the triangles have equal perimeters.
B. No; translations cannot cross an axis.
C. No; AB and DE have different lengths.
D. Yes; both triangles have a right angle.

Build the Bracket Layout

Apply motions in the stated order. All coordinates use the same grid units.

A first-round badge is reflected across the vertical line x = 1, then reflected across the vertical line x = 4. Which single motion has the same effect on the entire badge?

A. Translate 6 units right.
B. Rotate 180° about (1, 4).
C. Translate 3 units right.
D. Translate 6 units left.

To place a badge beside the winning score, rotate it 90° counterclockwise about (1, 1). One corner starts at (4, 1). Then translate the entire image 2 units left and 3 units down.

The corner's final coordinates are ( , ).

The triangular badge ABC must move to D(−2, 3), E(−2, 5), and F(−5, 3), with A → D, B → E, and C → F. Which sequence works?

A. Rotate 90° clockwise about the origin, then translate 5 units left and 2 units up.
B. Rotate 90° counterclockwise about the origin, then translate 5 units left and 2 units up.
C. Rotate 90° counterclockwise about the origin, then translate 5 units right and 2 units down.
D. Rotate 180° about the origin, then translate 1 unit left and 2 units up.

A quarterfinal badge is reflected across the y-axis, then translated 3 units up. A corner of its final image is (−5, 2).

What were that corner's original coordinates? ( , )

The tournament's triangular overtime marker has vertices (−2, −1), (1, −1), and (−2, 3). Which proposed replacement is congruent to it? Vertices may correspond in any order.

A. The replacement has vertices (2, 2), (2, 5), and (6, 2).
B. The replacement has vertices (0, 0), (4, 0), and (0, 4).
C. The replacement has vertices (0, 0), (3, 0), and (0, 5).
D. The replacement has vertices (0, 0), (6, 0), and (0, 8).

Verify the Final Layout

Check the whole figure, not just one point. Use preserved lengths and corresponding vertices as evidence.

10.

Two copies of a score marker fit into opposite sides of the bracket. Which sequence maps every original vertex to its target?

Opposite-Side Marker
Vertex	Original	Target
P → P′	(−1, 2)	(4, −1)
Q → Q′	(2, 2)	(1, −1)
R → R′	(−1, 4)	(4, 1)

A. Reflect across the y-axis, then translate 3 units right and 3 units up.
B. Reflect across the y-axis, then translate 3 units right and 3 units down.
C. Rotate 180° about the origin, then translate 3 units right and 3 units down.
D. Reflect across the x-axis, then translate 3 units right and 3 units down.

11.

A score badge is first reflected across the x-axis and then across the y-axis. Select every statement that must be true.

The final badge is congruent to the original.Every vertex returns to its starting position.The sequence is equivalent to a 180° rotation about the origin.Every side becomes twice as long.Corresponding angles have equal measures.

12.

The championship score panel uses rectangular badge ABCD. A designer rotates it 180° about the origin. Which statement describes the result?

A. The outline turns vertical, and A moves to D's original position.
B. The outline stays in place, and every labeled vertex stays fixed.
C. The outline stays in place, and A moves to C's original position.
D. The outline moves right, and A moves to B's original position.

13.

A score badge has A(−4, −3), B(−1, −3), and C(−4, −1). First reflect it across the x-axis. Then translate it only horizontally so that the image of A is (2, 3).

How many units right must the reflected badge move? units
What is the final x-coordinate of the image of B?

14.

Luis checks two triangular score badges using the table. He says, “Translating 3 units right maps A to D, so that translation maps the entire badge correctly.” Explain why his check is incomplete. Then describe a rigid-motion sequence that maps A → D, B → E, and C → F.