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. Mere draws a quadrilateral on a coordinate plane with vertices at A(11, 2), B(19, 2), C(19, 10), and D(11, 10). She reflects the quadrilateral across the line y = x, and then translates the reflected shape 7 units to the left and 4 units down. What are the coordinates of the final position of vertex C (originally at (19, 10)) after both transformations?
3. A triangle with vertices at (5, -3), (8, 4), and (-2, 6) is reflected across the x-axis. What are the coordinates of the reflected vertex that was originally at (8, 4)?

…and 4 more problems

1. A triangle with vertices at (6, 4), (9, 1), and (2, 7) is reflected across the x-axis. What are the coordinates of the reflected vertex that was originally at (9, 1)?
2. Liam is designing a triangular garden plot. He places markers at points A(2, 3), B(5, 7), and C(8, 3) on a coordinate grid. He wants to create a second plot that is congruent to the first by applying a sequence of rigid motions: first reflecting the triangle across the y-axis, then translating it 4 units down. What are the coordinates of the vertices of the second triangular plot after these transformations?
3. (3x + 2)² - (2x - 1)² = ?

…and 4 more problems

1. 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)?
2. Liam is designing a triangular logo for his robotics team. He creates triangle ABC with vertices at A(2,1), B(5,1), and C(3,4). To test different placements, he performs a sequence of rigid motions: first a translation 3 units right and 2 units up, then a reflection across the x-axis, and finally a 90° counterclockwise rotation about the origin. What are the coordinates of the final position of vertex C after all these transformations?
3. Liam is designing a triangular garden plot using congruent triangles. He places triangle ABC with vertices at A(2, 3), B(5, 3), and C(2, 7). He wants to create a congruent triangle DEF by applying a sequence of rigid motions: first a translation 4 units right and 2 units down, then a reflection across the x-axis. What are the coordinates of the final triangle's vertices?

…and 4 more problems