![]() Using the graph, we can see that this is a vertical displacement of four units downwards. Now let’s do the same to find the vertical displacement. This is the horizontal displacement of the ray □□. Because we are going from point □ to point □, we subtract the □-coordinate of □ from that of □, which also gives us two. We can also see this if we use the coordinates of □ and □ directly. And this is a positive value of two units because the direction is to the right. Since we are going from □ to □, the horizontal displacement will be two units. We can now determine the horizontal and vertical displacement between □ and □. We can join □ and □ to create the ray □□. We can then plot the points □ at coordinates negative three, negative two and □ at coordinates negative one, negative six. So here we have a copy of the grid with the line segment □□. ![]() And it might be useful to draw out this line segment □□ onto a larger grid so we can fit in all the important coordinates onto it. Whatever the displacement is on the given ray □□ in the question will be the same displacement, or the same translation, that we must apply to the line segment □□. As we know the direction - we’re going from □ to □ - then we can see how knowing two points and the direction of travel between them will allow us to determine the horizontal and vertical displacement that this must be. However, here, we are told the translation in terms of a ray from □ to □. And generally this will be given to us in these terms. We can recall that any translation can be thought of as a change in the horizontal and vertical displacement. And we are told that this line segment is translated. In the figure, we can see that the line segment □□ has been drawn on the coordinate grid. ![]() Or option (D) □ prime with coordinates negative one, eight, □ prime with coordinates one, three. Option (C) □ prime with coordinates three, zero, □ prime with coordinates negative one, one. Option (B) □ prime with coordinates negative three, six, □ prime with coordinates five, negative five. Which of the following coordinates represent the line segment □□ after a geometric translation of □□ in the direction of ray □□, where □ has coordinates negative three, negative two and □ has coordinates negative one, negative six, given that □ has coordinates one, four and □ has coordinates three, negative one? Option (A) □ prime with coordinates three, zero, □ prime with coordinates five, negative five.
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