WEBVTT
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Dilate triangle 𝐴𝐵𝐶 from the origin by a scale factor two, and state the coordinates of the image.
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We’re going to dilate or enlarge our triangle, and the centre that we’re going to use is the origin.
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That’s the point whose coordinates are zero, zero, as shown Now, we’re going to use a scale factor of two.
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That means each dimension of our triangle will be twice the size.
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It will double.
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But it’s important that each coordinate is double the distance, twice the distance, away from the centre of enlargement.
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And so, to achieve the dilation in the correct place, we might look to draw some rays.
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Each ray passes through the origin and a vertex of the triangle and we could, if we so wished, measure the distance of each vertex from the origin and then double that distance along that ray.
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So, for example, let’s take vertex 𝐶.
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It’s two units away from the origin horizontally.
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Which means the image of 𝐶 will be four units away from the origin horizontally, taking us to a point with coordinates negative four, zero.
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And I’ve written 𝐶 dash to show that this is the image of 𝐶.
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It’s the dilation.
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But what about point 𝐴?
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Well, to get from zero to point 𝐴, we move five units horizontally in the negative direction and then two units vertically upwards.
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And so, this is a little bit tricky because when we double these distances, we end up moving 10 units horizontally and four units up.
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That must take us to the point with cartesian coordinates negative 10, four.
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And unfortunately, since this’s come off of our grid, we can only estimate its location.
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Let’s repeat this with point 𝐵.
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This time to move from the origin to point 𝐵, we move three units horizontally in the negative direction and then four units up.
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And so, to get from zero to the image of 𝐵, we’re going to double these distances.
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We’re going to move six units left and eight units up.
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That takes us to the point with coordinates negative six, eight.
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And so, we add the image of 𝐴𝐵𝐶, its dilation, as shown.
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And if we were to measure each of the sides of this triangle, we would see that each side is now double the length of the original triangle.
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The coordinates of the image of 𝐴𝐵𝐶 are negative 10, four; negative six, eight; and negative four, zero.