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?