Describe the series of transformations that occur have occurred to move the triangle and quadrant 4 to the each triangle in quadrant two to show that the triangles are congruent.

Question

Original position was G (-5, 5) E (-1, 3) H (-5, 3)
New position is G (3, 3) E (7, 1) H (3, 1)
The options are
A reflections then translation
B translation, then rotation
C rotation then reflection
D rotation, then translation

Answer 1

The series of transformations that have occurred to move the triangle in quadrant 4 to the triangle in quadrant 2 are:

D) rotation, then translation

Explanation:

Step 1: Rotation
The first transformation that occurred is a rotation. The triangle is rotated 180 degrees about the origin (0,0). This moves the original triangle in quadrant 4 to quadrant 2. The new coordinates after rotation are:

G' (-5, -5)
E' (-1, -3)
H' (-5, -3)

Step 2: Translation
The second transformation is a translation. The triangle is moved 8 units in the positive x-direction and 2 units in the positive y-direction. This gives us the final new position of the triangle in quadrant 2:

G (3, 3)
E (7, 1)
H (3, 1)

Therefore, the correct answer is D) rotation, then translation.