A line segment has endpoints at $(7, 6)$ $(7 ,6 )$ and $(5, 3)$ $(5 ,3 )$ . If the line segment is rotated about the origin by $π$ $pi$ , translated horizontally by $- 4$ $- 4$ , 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 $(7, 6)$ $(7 ,6 )$ and $(5, 3)$ $(5 ,3 )$ . If the line segment is rotated about the origin by $π$ $pi$ , translated horizontally by $- 4$ $- 4$ , and reflected about the y-axis, what will the line segment's new endpoints be?

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Answer 1 · 2017-02-09T12:12:44

$(11, - 6) and (9, - 3)$ $(11,-6)" and " (9,-3)$

Explanation:

Since there are 3 transformations to be performed here, label the endpoints A(7 ,6) and B(5 ,3)

$First transformation - Under a rotation about origin of π$ $color(blue)"First transformation"- "Under a rotation about origin of "pi$

$a point (x, y) \to (- x, - y)$ $"a point "(x,y)to(-x,-y)$

Hence A(7 ,6) → A'(-7 ,-6) and B(5 ,3) → B'(-5 ,-3)

$color(blue)"Second transformation "-"Under a translation" ((-4),(0))$

$"a point "(x,y)to(x-4,y)$

Hence A'(-7 ,-6) → A''(-11 ,-6) and B'(-5 ,-3) →B''(-9 ,-3)

$color(blue)"Third transformation"-" Under a reflection in the y-axis"$

$"a point "(x,y)to(-x,y)$

Hence A''(-11 ,-6) → A'''(11 ,-6) and B''(-9 ,-3) → B'''(9 ,-3)

After all 3 transformations.

$(7,6)to(11,-6)" and " (5,3)to(9,-3)$

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A line segment has endpoints at $(7, 6)$ $(7 ,6 )$ and $(5, 3)$ $(5 ,3 )$ . If the line segment is rotated about the origin by $π$ $pi$ , translated horizontally by $- 4$ $- 4$ , and reflected about the y-axis, what will the line segment's new endpoints be?

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Explanation:

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Humanities

... and beyond

A line segment has endpoints at (7 ,6 )(7,6)(7 ,6 ) and (5 ,3 )(5,3)(5 ,3 ). If the line segment is rotated about the origin by pi π pi , translated horizontally by - 4 −4 - 4 , 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 $(7, 6)$ $(7 ,6 )$ and $(5, 3)$ $(5 ,3 )$ . If the line segment is rotated about the origin by $π$ $pi$ , translated horizontally by $- 4$ $- 4$ , and reflected about the y-axis, what will the line segment's new endpoints be?