Question

11. Persevere in Problem Solving Emma and Tony are playing a game. Each draws a triangle

Answer 1

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, $T_{(6, \ -5)}$

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, $T_{(6, \ -5)}$

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, $T_{(-10, \ 8)}$

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, $T_{(-10, \ 8)}$

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:

brainly.com/question/12187315