Question

after the first step of a play, player three is at (-1.5,0) and player 4 is at (1,0.5) write a rule to describe The translations of players three and four from their starting positions to the new positions

Answer 1

1. rule for 3: (x, y) ⇒ (x +4.5, y -1); rule for 4: (x, y) ⇒ (x -4, y +1)

2. 3: (-5.5, -2); 4: (4, -1.5)

Explanation:

1.

The amount of translation that occurred from the initial position to the final position can be found by subtracting the initial from the final position.

player 3: (-1.5, 0) -(-6, 1) = (-1.5 +6, 0 -1) = (4.5, -1) . . . step 1 translation

This translation is added to (x, y) in the transformation rule:

(x, y) ⇒ (x +4.5, y -1) . . . . player 3 rule for step 1

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Similarly, the rule for player 4 is found to be ...

player 4: (1, 0.5) -(5, -0.5) = (1 -5, 0.5 +0.5) = (-4, 1) . . . step 1 translation

(x, y) ⇒ (x -4, y +1) . . . . player 4 rule for step 1

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2.

The new positions are found by applying the rules to the step 1 positions.

player 3:

(x, y) ⇒ (x -4, y -2)

3'(-1.5, 0) ⇒ 3''(-1.5 -4, 0 -2) = 3''(-5.5, -2) . . . position after step 2

player 4:

(x, y) ⇒ (x +3, y -2)

4'(1, 0.5) ⇒ 4''(1 +3, 0.5 -2) = 4''(4, -1.5) . . . position after step 2