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Tournament Bracket: Score Badge Moves

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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.

1.
Select every edit that guarantees a score badge remains congruent to its original.

2.
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?−5−4−3−2−1123450−5−4−3−2−112345ABC
Question 2 options
3.
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

4.
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
VertexOriginalReplacement
A → D(−3, −2)(1, 1)
B → E(0, −2)(5, 1)
C → F(−3, 2)(1, 4)
Question 4 options

Build the Bracket Layout

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

5.
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?
Question 5 options
6.
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 (, ).

7.
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?−6−5−4−3−2−11234560−6−5−4−3−2−1123456ABC
Question 7 options
8.
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? (, )

9.
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.
Question 9 options

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
VertexOriginalTarget
P → P′(−1, 2)(4, −1)
Q → Q′(2, 2)(1, −1)
R → R′(−1, 4)(4, 1)
Question 10 options
11.
A score badge is first reflected across the x-axis and then across the y-axis. Select every statement that must be true.

12.
The championship score panel uses rectangular badge ABCD. A designer rotates it 180° about the origin. Which statement describes the result?−5−4−3−2−1123450−5−4−3−2−112345ABCD
Question 12 options
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.
Final Badge Check
CorrespondenceOriginalTarget
A → D(−2, 1)(1, 1)
B → E(0, 1)(1, 3)
C → F(−2, 4)(−2, 1)