A line segment has endpoints at $(5, 8)$ $(5 ,8 )$ and $(7, 4)$ $(7 ,4)$ . If the line segment is rotated about the origin by $π$ $pi$ , translated horizontally by $- 1$ $-1$ , and reflected about the y-axis, what will the line segment's new endpoints be?

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A line segment has endpoints at $(5, 8)$ $(5 ,8 )$ and $(7, 4)$ $(7 ,4)$ . If the line segment is rotated about the origin by $π$ $pi$ , translated horizontally by $- 1$ $-1$ , and reflected about the y-axis, what will the line segment's new endpoints be?

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Answer 1 · 2016-01-21T13:45:39

$(6, - 8), (8, - 4)$ $(6,-8),(8,-4)$

Explanation:

We can create a rule for this transformation.

Assume the original endpoints of the segment can be described as $(x, y)$ $color(red)((x,y)$ .

The first way in which the segment is manipulated is with a rotation of $π$ $pi$ , or $180^{\circ}$ $180^@$ . This translates by taking the opposite of the $x$ $x$ and $y$ $y$ values of the point, or our new "rule" for this point in the transformation: $(- x, - y)$ $color(red)((-x,-y)$

The endpoints are then translated horizontally by $- 1$ $-1$ . Horizontal movement corresponds to the $x$ $x$ coordinate, whereas vertical corresponds to the $y$ $y$ coordinate. Since this has been horizontally shifted, the new rule, working off the most previous rule, is: $(- x - 1, - y)$ $color(red)((-x-1,-y)$

The final transformation is a reflection over the $y$ $y$ axis, which means that the $x$ $x$ coordinate's sign is flipped: $(x + 1, - y)$ $color(red)((x+1,-y)$

This is the rule for the entire transformation. Apply it to the points $(5, 8)$ $(5,8)$ and $(7, 4)$ $(7,4)$ .

$(5, 8) \to (6, - 8)$ $(5,8)rarr(6,-8)$

$(7, 4) \to (8, - 4)$ $(7,4)rarr(8,-4)$

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A line segment has endpoints at $(5, 8)$ $(5 ,8 )$ and $(7, 4)$ $(7 ,4)$ . If the line segment is rotated about the origin by $π$ $pi$ , translated horizontally by $- 1$ $-1$ , and reflected about the y-axis, what will the line segment's new endpoints be?

1 Answer

Explanation:

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A line segment has endpoints at (5,8)(5 ,8 ) and (7,4)(7 ,4). If the line segment is rotated about the origin by πpi , translated horizontally by −1-1 , and reflected about the y-axis, what will the line segment's new endpoints be?

1 Answer

Explanation:

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A line segment has endpoints at $(5, 8)$ $(5 ,8 )$ and $(7, 4)$ $(7 ,4)$ . If the line segment is rotated about the origin by $π$ $pi$ , translated horizontally by $- 1$ $-1$ , and reflected about the y-axis, what will the line segment's new endpoints be?