WEBVTT
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Reflect triangle 𝐴 in the 𝑦-axis and then in the 𝑥-axis.
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Which triangle is its image?
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Let’s begin by reflecting triangle 𝐴, that’s this one up here, in the 𝑦-axis, which is this vertical line.
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We know that when we reflect a shape in a mirror line, the shape will end up exactly the same distance from the mirror line, but on the other side.
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And it will be sort of flipped.
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And one way we can find the image after reflection is to do this vertex by vertex.
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Let’s begin with this vertex on triangle 𝐴.
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We measure the perpendicular distance of this vertex from the mirror line, and that’s two units.
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We now come the exact same distance out of the mirror line on the other side.
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And when we do, we see that the vertex is on triangle 𝐶.
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And so, we can probably deduce that the image of triangle 𝐴 after its first reflection is triangle 𝐶.
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But let’s double-check this with another vertex.
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Let’s take this vertex at the top of our triangle.
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Once again, we measure the perpendicular distance of this vertex from the mirror line, and that’s three units.
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We come out the other side of the mirror line the exact same distance, and we end up with the second vertex at 𝐶.
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And in fact, if we did that with the third vertex, we’d end up with the third vertex at 𝐶.
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And so, the image of triangle 𝐴 after the first reflection is triangle 𝐶.
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But then we’re told this triangle is reflected in the 𝑥-axis, and this is this horizontal line.
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And so once again, we know that the image of 𝐶 after the reflection will be the exact same distance away from the line directly at the other side.
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And so we measure the perpendicular distance of our first vertex from the mirror line, and it’s two units once again.
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We carry on out the other side of the mirror line at the same distance, and we end up at this vertex at point two, negative two.
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We can do the same with our other vertices, and we end up with a vertex at point five, negative three and one at three, negative five.
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And so, the image of 𝐶 after its reflection is triangle 𝐷.
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And so, we could therefore say that when we reflect triangle 𝐴 in the 𝑦-axis and then in the 𝑥-axis, the triangle that is its image is triangle 𝐷.
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Now, in fact, this wasn’t necessarily the quickest way to achieve this.
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And this is because if we reflect a shape in one axis and then reflect it in the other, that’s the same as rotating that shape 180 degrees about the origin or the point zero, zero.
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If we look at 𝐴, if we rotate that 180 degrees about this point, we do indeed get to triangle 𝐷.
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Either method is perfectly valid as long as we get the answer 𝐷.