WEBVTT
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Consider π΄-coordinate negative one, negative two and π΅-coordinate negative seven, seven.
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Find the coordinates of πΆ, given that πΆ is on the ray π΄π΅, but not on the segment π΄π΅ and π΄πΆ equals two πΆπ΅.
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So letβs start this question by considering our two coordinates.
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If itβs helpful, we could plot these two points on a coordinate grid.
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But sometimes, itβs sufficient just to plot their relative position to each other.
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Here, weβre told that thereβs a ray π΄π΅.
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That means that the line starts at π΄, goes through π΅, and continues indefinitely.
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Weβre told that thereβs a coordinate πΆ, which is on the ray π΄π΅, but not on the segment π΄π΅, which means that πΆ isnβt between π΄ and π΅.
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So we can draw it on the line beyond π΄π΅.
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Weβre told that π΄πΆ equals two πΆπ΅.
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This means that if we said π₯ was the length of πΆπ΅, then π΄πΆ must be two times that, giving us two π₯.
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At this point, we donβt know the length π₯ or the length πΆπ΅.
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But given we know the coordinates of π΄ and π΅, we could work out the length π΄π΅, which would also be of a length π₯.
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An alternative way to consider this would be to think that the ratio of π΄π΅ to π΅πΆ would be one to one.
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So letβs now consider our length π΄π΅.
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And we can do this by considering how we go from π΄ to π΅ with our coordinates.
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If we look at the π₯-coordinate of point π΄ as negative one and we go to our π₯-coordinate of π΅, which is negative seven.
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This means that we would move negative six horizontally.
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If we consider our π¦-values, then we have negative two on our π΄-coordinate up to seven on our π΅-coordinate, which represents a move of nine vertically.
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So now as we know that the ratio of π΄π΅ to π΅πΆ is one to one.
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This means that the journey from π΅ to πΆ must also be negative six horizontally and nine vertically.
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So to find our π₯-value in coordinate πΆ, we go from the π₯-value in π΅, which is negative seven.
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And we subtract six since we had a negative six movement horizontally.
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So our π₯-value would be negative 13.
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For our π¦-values then, our π¦-value of π΅ was at seven.
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And we must add nine since we move nine vertically.
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And since seven add nine is 16, this gives us the π¦-value of 16.
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So the coordinate of πΆ is negative 13, 16.