Describe the sequence of steps, used to move the triangle to quadrant four to the triangle in quadrant two to show the triangles are congruent. Original position was A (-5, 5) B (-5, 3) C (-1, 3) new position A (3, 3) B (3, 1) C (7, 1)
A reflection then translation
B translation, then transformation
C translation, then reflection
D rotation, then translation
The correct sequence of steps to move the triangle in quadrant four to the triangle in quadrant two to show congruence is:
A) Reflection, then translation.
1. Start with the original position of the triangle in quadrant four:
Triangle ABC: A(-5, 5), B(-5, 3), C(-1, 3)
2. Perform a reflection of the triangle across the y-axis to move it to quadrant one:
Triangle A'B'C': A'(5, 5), B'(5, 3), C'(1, 3)
3. Then, perform a translation to move the triangle from quadrant one to quadrant two:
Triangle A''B''C'': A''(3, 3), B''(3, 1), C''(7, 1)
By following these steps, you would show that the triangles are congruent.
C) translation, then reflection.
The sequence of steps used to move the triangle from quadrant four to quadrant two can be described as follows:
1) Translation: The triangle is moved to the right by 8 units and down by 2 units to the new position.
- A (-5, 5) is translated to (3, 3)
- B (-5, 3) is translated to (3, 1)
- C (-1, 3) is translated to (7, 1)
2) Reflection: The triangle is then reflected across the y-axis to obtain the final position.
- A (3, 3) is reflected to (-3, 3)
- B (3, 1) is reflected to (-3, 1)
- C (7, 1) is reflected to (-7, 1)
Therefore, the correct answer is C) translation, then reflection.