Video: Pack 3 • Paper 2 • Question 2

Pack 3 • Paper 2 • Question 2

03:38

Video Transcript

The shape 𝐴 is graphed below. Part a) reflect shape 𝐴 in the 𝑥-axis. Label the new shape 𝐵. Part b) Rotate shape 𝐵 90 degrees anticlockwise about the origin. Label the new shape 𝐶.

The first part of our question asked us to reflect shape 𝐴 in the 𝑥-axis or the horizontal axis. In order to do this, we can use tracing paper. Alternatively, we can see how far shape 𝐴 is away from the 𝑥-axis. The coordinate negative two, two is two squares away from the 𝑥-axis. This means that the reflection of this point must be two squares below the 𝑥-axis.

Our first point has coordinates negative two, negative two. The coordinate negative one, three is three squares away from the 𝑥-axis. Therefore, its reflection must be three squares below the 𝑥-axis. This means that the second corner or vertex of our shape has coordinates negative one, negative three.

We could repeat this process with the coordinates negative one, five and negative two, four. They would be reflected to negative one, negative five and negative two, negative four, respectively. This means that the four corners or vertices of our new shape are negative one, negative five; negative two, negative four; negative two, negative two; and negative one, negative three. Joining these four coordinates gives us shape 𝐵, the reflection of shape 𝐴 in the 𝑥-axis.

The second part of our question asked us to rotate shape 𝐵 90 degrees anticlockwise about the origin. The origin has coordinates zero, zero. Once again, we could use tracing paper to rotate shape 𝐵 90 degrees anticlockwise. If we consider the vertex of shape 𝐵, negative one, negative three, this vertex has to move one square to the right and three squares up to reach the origin. Rotating this 90 degrees anticlockwise takes us to the coordinates three, negative one — three squares to the right and one square down.

We can repeat this process with the other coordinates. Negative two, negative two is rotated to the coordinate two, negative two. The coordinate negative two, negative four is rotated to the coordinate four, negative two. And finally, the coordinate negative one, negative five is rotated 90 degrees anticlockwise to the coordinate five, negative one. Joining these four coordinates or vertices gives us shape 𝐶, the rotation of shape 𝐵 90 degrees anticlockwise about the origin. The coordinates of the vertices of shape 𝐶 are three, negative one; two, negative two; four, negative two; and five, negative one.

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