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11. Persevere in Problem Solving Emma and Tony are playing a game. Each draws a triangle
on a coordinate grid. For each turn, Emma chooses either the horizontal or vertical value for
a vector in component form. Tony chooses the other value, alternating each turn. They each
have to draw a new image of their triangle using the vector with the components they chose
and using the image from the prior turn as the preimage. Whoever has drawn an image in
each of the four quadrants first wins the game.
Emma's initial triangle has the coordinates (3, 0), (-4, —2), (-2, -2) and Tony's initial
triangle has the coordinates (2, 4), (2, 2), (4, 3). On the first turn the vector (6, –5) is used
and on the second turn the vector (-10, 8) is used. What quadrant does Emma need to
translate her triangle to in order to win? What quadrant does Tony need to translate his
triangle to in order to win? Emma needs to translaté

Respuesta :

Transformations in the coordinate plane maps preimage coordinate points to the coordinate points of the image

  • The quadrant Emma needs to translate her triangle to in order to win are; 3rd and 1st quadrants
  • The quadrant Tony needs to translate his image to in order to win is; 3rd quadrant

The reason the above values are correct are as follows:

The given parameter are;

The coordinates of Emma's initial triangle are; (3, 0), (-4, -2), (-2, -2)

Tony's initial triangle coordinates are; (2, 4), (2, 2), (4, 3)

The vector used on the first turn is <6, -5>, which gives;

Emma's first transformation, [tex]T_{(6, \ -5)}[/tex]

1st quadrant (3, 0) → 4th quadrant (9, -5)

3rd quadrant (-4, -2) → 4th quadrant (2, -7)

3rd quadrant (-2, -2) → 4th quadrant (4, -5)

Tony's first transformation, [tex]T_{(6, \ -5)}[/tex]

1st quadrant (2, 4) → 4th quadrant (8, -1)

1st quadrant (2, 2) → 4th quadrant (8, -3)

1st quadrant (4, 3) → 4th quadrant (10, -2)

Emma's second transformation, [tex]T_{(-10, \ 8)}[/tex]

4th quadrant (9, -5) → 2nd quadrant (-1, 3)

4th quadrant (2, -7) → 2nd quadrant (-8, 1)

4th quadrant (4, -5) → 2nd quadrant (-6, 3)

Tony's second transformation, [tex]T_{(-10, \ 8)}[/tex]

4th quadrant (8, -1) → 2nd quadrant (-2, 7)

4th quadrant (8, -3) → 2nd quadrant (-2, 5)

4th quadrant (10, -2) → 1st quadrant (0, 6)

From the above translation transformations, Emma has drawn an image in the 4th and 2nd quadrant, and would needs to draw an image in the 3rd and 1st quadrant

Similarly, from the above values, Tony has drawn an image in the 4th quadrant, 2nd quadrant and 1st quadrant, therefore Tony needs to translate to only the 3rd quadrant in order to win

Learn more about transformations in the coordinate plane here:

https://brainly.com/question/12187315

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