Use the image to answer the question.

Question

Two triangles are drawn on a coordinate plane. Triangle A B C is drawn with a solid line and is in quadrant 3. Triangle A prime B prime C prime is drawn with a dotted line and is in quadrant 4.

Describe the transformation in the diagram.

(1 point)
Responses

90°
clockwise rotation about the origin
90 degrees clockwise rotation about the origin

90°
counterclockwise rotation about the origin
90 degrees counterclockwise rotation about the origin

270°
counterclockwise rotation about the origin
270 degrees counterclockwise rotation about the origin

180°
counterclockwise rotation about the origin

Answer 1

The transformation described involves two triangles located in different quadrants on a coordinate plane. Triangle ABC is in quadrant 3, and triangle A'B'C' is in quadrant 4.

To determine the appropriate transformation, we note that moving from quadrant 3 (where both x and y coordinates are negative) to quadrant 4 (where x is positive and y is negative) typically involves a rotation.

A 90° clockwise rotation about the origin will move points from quadrant 3 to quadrant 4. This is because in a 90° clockwise rotation:

• The x-coordinate and y-coordinate are transformed as follows:
  • (x, y) → (y, -x)

For points in quadrant 3, this transformation would indeed place points in quadrant 4.

Therefore, the correct transformation is:

90° clockwise rotation about the origin.