Congruence Concepts Worksheets Grade 8

1. A triangle has vertices at A(1, 2), B(4, 2), and C(1, 5) on a coordinate plane. The triangle is first rotated 90° counterclockwise about the origin, then reflected across the x-axis. What are the coordinates of the final position of vertex C after both transformations?
2. Liam is designing a triangular logo for his robotics team. He creates triangle ABC with vertices at A(2, 3), B(5, 1), and C(7, 4). He wants to create a congruent triangle DEF by applying a sequence of rigid motions. First, he reflects triangle ABC across the y-axis, then rotates the resulting triangle 90° counterclockwise about the origin, and finally translates it 3 units right and 2 units up. What are the coordinates of vertex D in the final triangle DEF?
3. A triangle with vertices at (4, -2), (9, 6), and (-3, 8) is reflected across the x-axis. What are the coordinates of the reflected vertex that was originally at (9, 6)?

…and 4 more problems

1. A triangle with vertices at (6, 8), (10, 12), and (4, 15) is reflected across the x-axis. What are the coordinates of the reflected vertex that was originally at (10, 12)?
2. (3x + 2)² - (2x - 1)² = ?
3. √(x² - 10x + 25) = 8

…and 5 more problems

1. Liam is designing a triangular garden plot. He places stakes at points A(2, 3), B(5, 7), and C(8, 3). His friend Noah wants to create a congruent triangular plot adjacent to it by applying a sequence of rigid motions: first a translation 4 units right and 2 units up, then a reflection across the vertical line x=9. What are the coordinates of the vertices of Noah's triangular garden plot after applying these transformations?
2. A triangle with vertices at (4, 7), (9, 2), and (1, 5) is reflected across the y-axis. What are the coordinates of the reflected vertex that was originally at (9, 2)?
3. A triangle with vertices at (8, 5), (12, 9), and (6, 13) is reflected across the y-axis. What are the coordinates of the reflected vertex that was originally at (12, 9)?

…and 4 more problems