Video: Pack 3 • Paper 3 • Question 9

Pack 3 • Paper 3 • Question 9

02:55

Video Transcript

The graph below shows a trapezium 𝐴 on a grid. Jack rotates trapezium 𝐴 clockwise about the origin by 90 degrees to get trapezium 𝐵. He then reflects trapezium 𝐵 in the 𝑥-axis to get trapezium 𝐶. Samantha reflects trapezium 𝐴 in the line 𝑥 equals minus three to get trapezium 𝐷. She then rotates trapezium 𝐷 about the origin 180 degrees to get trapezium 𝐸. Samantha says that trapezium 𝐶 and trapezium 𝐸 are identical. Is Samantha correct?

If we firstly consider Jack, Jack’s first step was to rotate trapezium 𝐴 clockwise about the origin by 90 degrees. Rotating a trapezium gives us vertices of 𝐵 of two, two; four, two; four, three; and two, four. Jack’s next step was to reflect trapezium 𝐵 in the 𝑥-axis. Well, the 𝑥-axis is the horizontal axis. Reflecting trapezium 𝐵 in the 𝑥-axis gives us vertices of trapezium 𝐶 of two, minus two; four, minus two; four, minus three; and two, minus four.

If we now consider Samantha, her first step was to reflect trapezium 𝐴, which has vertices minus two, two; minus two, four; minus four, two; and minus three, four in the line 𝑥 equals minus three. The line 𝑥 equals minus three is a vertical line that cuts minus three on the 𝑥-axis. Reflecting trapezium 𝐴 in this line gives us vertices of trapezium 𝐷 with coordinates minus four, two; minus four, four; minus two, two; and minus three, four. Finally, Samantha rotated trapezium 𝐷 about the origin 180 degrees. Rotating trapezium 𝐷 180 degrees about the origin gives us trapezium 𝐸 with vertices two, minus two; four, minus two; four, minus four; and three, minus four.

As trapezium 𝐶 and trapezium 𝐸 are not identical, we can say that Samantha is not correct. The two transformations performed by Jack and the two transformations performed by Samantha did not end up in the same place.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.