WEBVTT
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Determine the coordinates of the image of point 𝐵 of quadrilateral 𝐴𝐵𝐶𝐷 after a translation five units left and three units down.
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Now a translation is a very specific sort of transformation.
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And basically you’re moving the shape; you’re picking it up and you’re moving it somewhere else.
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But importantly the shape stays exactly the same size and the same orientation.
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So you don’t rotate it at all; you’re just literally keeping it as it is, but moving it left and right or up and down.
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And also all interior angles stay the same size.
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So we’re gonna be picking up this shape 𝐴𝐵𝐶𝐷 and moving it five units to the left and three units down.
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And we’re specifically interested in what happens to point 𝐵.
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Well 𝐵 starts off with an 𝑥-coordinate of negative nine and a 𝑦-coordinate of negative eight.
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And along with every other point on that shape, it’s gonna move five units to the left and three units down.
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This means that we’re gonna be subtracting five units from the 𝑥-coordinate and subtracting three units from the 𝑦-coordinate.
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Now the labeling convention for a transformed point is to put a dash or a prime mark on it.
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So 𝐵 is gonna be transformed to point 𝐵 dashed.
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And the 𝑥-coordinate is gonna be negative nine take away another five, which is negative fourteen.
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And the 𝑦-coordinate is gonna be negative eight take away another three, so that’s negative eleven.
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So the answer is that the coordinates of the image of point 𝐵, the translated point, the transformed point — let’s call it 𝐵 dashed — are gonna be negative fourteen for the 𝑥-coordinate and negative eleven for the 𝑦-coordinate.