WEBVTT
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The diagram shows shape A and shape B.
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Shape A can be mapped to shape B by a single transformation.
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Josh says that shape A can only be mapped to shape B by reflecting it in the 𝑦-axis.
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Is Josh correct?
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Tick the correct box.
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Yes or no.
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Then give a reason for your answer.
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In this case, Josh is not correct.
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It is certainly true that shape A reflected over the 𝑦-axis would be shape B.
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However, there’s another transformation that can get us from A to B.
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We can get from shape A to shape B by translating shape A seven units to the left.
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The reason Josh is not correct is that shape A can also be translated seven units left to give shape B.
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Part b) says, “The diagram shows triangles A and B.
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Triangle A is mapped to triangle B by a combination of two transformations.
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The first transformation is a reflection in the 𝑥-axis.
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Fully describe the second transformation.”
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Before we describe the second transformation, let’s go ahead and graph the first transformation, a reflection in the 𝑥-axis on our grid.
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Reflecting over the 𝑥-axis means making the 𝑦-coordinate negative.
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If we began with the point at negative eight, two, a reflection of the 𝑥-axis changes that to negative eight, negative two.
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Negative four, two becomes negative four, negative two and negative six, positive six becomes negative six, negative six.
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Connecting the dots gives us A prime.
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The second transformation is what is happening between A prime and B.
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Triangle A prime has a base of four units, while triangle B has a base of two units.
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Triangle B is half the size of triangle A prime.
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And we write that as an enlargement by a scale factor of one-half.
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We need to be careful here because anytime we have an enlargement, we’ll also have a centre.
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The centre is the place where these rays all cross.
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In our case, we have a centre at the origin.
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We can call the centre point 𝑂.
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To make these rays, we draw lines from corresponding vertices for all three sets of vertices.
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And their intersection — in this case at the origin — is the centre of your enlargement.