Tournament Bracket: Score Badge Moves
0 / 14Tournament 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?
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?
| Vertex | Original | Replacement |
|---|---|---|
| A → D | (−3, −2) | (1, 1) |
| B → E | (0, −2) | (5, 1) |
| C → F | (−3, 2) | (1, 4) |
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?
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?
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.
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?
| Vertex | Original | Target |
|---|---|---|
| P → P′ | (−1, 2) | (4, −1) |
| Q → Q′ | (2, 2) | (1, −1) |
| R → R′ | (−1, 4) | (4, 1) |
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?
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.
| Correspondence | Original | Target |
|---|---|---|
| A → D | (−2, 1) | (1, 1) |
| B → E | (0, 1) | (1, 3) |
| C → F | (−2, 4) | (−2, 1) |