WEBVTT
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A triangle has vertices at the points one, one; seven, one; and one, two.
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The image of this triangle has vertices at the points negative one, one; negative one, seven; and negative two, one.
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Which transformation has taken place?
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There are a couple of ways to answer this question.
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The first is to sketch this out on a coordinate grid.
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Let’s put each vertex in turn.
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The first vertex is the vertex one, one, which is here.
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We have a vertex at seven, one, which is here, and one at one, two, which is here.
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And so, we have a right triangle located in the first quadrant.
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Let’s now plot the image of the triangle.
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The first vertex has coordinates negative one, one, which is here.
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The next has coordinates negative one, seven, which is here.
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And the last has coordinates negative two, one, which is here.
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And so, we now have the original triangle and its image.
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So, we need to decide which transformation has taken place.
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We can choose from reflections where the fl reminds us we flip a shape across the mirror line.
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We have rotations where the t reminds us that we turn the shape about a center for a given angle and in a given direction.
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When we dilate a shape, the l reminds us we make it larger or smaller.
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And we could translate a shape.
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And when we translate it, we slide it.
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So, are there any of these that we can instantly disregard?
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Well, yes.
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Firstly, the shapes are the same size, and so we can disregard dilations.
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We can dilate a shape and end up with a shape that’s the same size if we use a negative scale factor, in fact, a scale factor of negative one.
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But the orientation for that isn’t quite right.
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Similarly, when we translate a shape, we slide it.
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This means its orientation doesn’t change, just its position on the grid.
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And so, we’re disregarding translations, leaving us with reflections or rotations.
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When we reflect a shape, we flip it in a mirror line.
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Now there’s no way to draw a mirror line on our diagram so that when we flip it or reflect the original shape, we end up with the new one.
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And so, that leaves us with rotation.
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Now, actually, it does indeed look like this shape has been rotated.
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It’s been turned.
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If we look carefully, we see it’s been turned by 90 degrees in a counterclockwise direction.
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In fact, if we were to describe the full transformation, we could say this is a rotation by 90 degrees in a counterclockwise direction about the origin or center zero, zero.
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But we’re just being asked which transformation has taken place, and so the answer is rotation.