Question

Describe the series of transformations that have occurred to move the triangle in Quadrant IV to the triangle in Quadrant II to show that the triangles are congruent.
a)reflection, then translation
b)rotation, then translation
c)rotation, then reflection
d)transition, then rotation

Answer 1

The correct answer is c) rotation, then reflection.

To move the triangle in Quadrant IV to the triangle in Quadrant II, we can see that they have the same shape and orientation, just in different quadrants. Therefore, to show that they are congruent, we can use a combination of rotation and reflection.

First, we can rotate the triangle in Quadrant IV counterclockwise by 180 degrees around the origin. This will bring it to Quadrant I, but it will be upside down.

Next, we can reflect the triangle in Quadrant I across the x-axis. This will flip it vertically and move it to Quadrant II. The result will be the congruent triangle that matches the one in Quadrant II.

So, the correct series of transformations that have occurred to move the triangle in Quadrant IV to the triangle in Quadrant II is rotation, then reflection.