Some transformations are given in the table below. Determine if the statements about the transformations are true or false.

Question

Drag and drop either True or False into the box next to each statement.

True

False

TransformationTrue/FalsePoint W in quadrant II is reflected across the y-axis and then rotated 90° counterclockwise about the origin to get point W'. Point W' will be in quadrant II.Point X in quadrant III is reflected across the x-axis and then across the y-axis to get point X'. Point X' will be in quadrant II.A line segment PQ with endpoints at P(1, 8) and Q(5, –2) is reflected across the y-axis and translated up 6 units to get line segment P'Q' with endpoints P' and Q'. The coordinates for point Q' is (1, –2).A line segment KL with endpoints at K(–1, 3) and L(4, 5) is reflected across the x-axis and translated down 2 units to get line segment K'L' with endpoints K' and L'. Line segment KL and K'L' are parallel.

Answer 1

Let's analyze each statement one by one based on the transformations mentioned.

1. Statement: Point W in quadrant II is reflected across the y-axis and then rotated 90° counterclockwise about the origin to get point W'. Point W' will be in quadrant II.

   • Analysis: Reflecting a point in quadrant II across the y-axis will move it to quadrant I. Rotating a point in quadrant I (the new position after reflection) 90° counterclockwise will move it to quadrant IV.
   • Result: False

2. Statement: Point X in quadrant III is reflected across the x-axis and then across the y-axis to get point X'. Point X' will be in quadrant II.

   • Analysis: Reflecting point X across the x-axis moves it to quadrant II. Reflecting again across the y-axis will move it to quadrant I.
   • Result: False

3. Statement: A line segment PQ with endpoints at P(1, 8) and Q(5, –2) is reflected across the y-axis and translated up 6 units to get line segment P'Q' with endpoints P' and Q'. The coordinates for point Q' is (1, –2).

   • Analysis: Reflecting Q(5, -2) across the y-axis results in Q'(-5, -2). Translating up 6 units results in Q'(-5, 4).
   • Result: False

4. Statement: A line segment KL with endpoints at K(–1, 3) and L(4, 5) is reflected across the x-axis and translated down 2 units to get line segment K'L' with endpoints K' and L'. Line segment KL and K'L' are parallel.

   • Analysis: Reflecting K(–1, 3) across the x-axis gives K'(–1, -3) and L(4, 5) gives L'(4, -5). Note that the slopes of both segments will remain the same, hence they will be parallel.
   • Result: True

Now compiling the results:

• Point W' will be in quadrant II: False
• Point X' will be in quadrant II: False
• The coordinates for point Q' is (1, –2): False
• Line segment KL and K'L' are parallel: True

Thus, the final answers are:

1. False
2. False
3. False
4. True