A line segment has endpoints at $(3, 8)$ $(3 ,8 )$ and $(4, 6)$ $(4 ,6)$ . If the line segment is rotated about the origin by $\frac{π}{2}$ $(pi )/2$ , translated vertically by $- 6$ $-6$ , 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 $(3, 8)$ $(3 ,8 )$ and $(4, 6)$ $(4 ,6)$ . If the line segment is rotated about the origin by $\frac{π}{2}$ $(pi )/2$ , translated vertically by $- 6$ $-6$ , and reflected about the y-axis, what will the line segment's new endpoints be?

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Answer 1 · 2016-06-24T10:16:01

$(3, 8) \to (8, - 3) and (4, 6) \to (6, - 2)$ $(3,8)to(8,-3)" and " (4,6)to(6,-2)$

Explanation:

Since there are 3 transformations to be performed name the endpoints A(3 ,8) and B(4 ,6) so we can 'track' them.

First transformation: Under a rotation about the origin of $\frac{π}{2}$ $pi/2$

a point (x ,y) → (-y ,x)

hence A(3 ,8) → A'(-8 ,3) and B(4 ,6) → B'(-6 ,4)

Second transformation: Under a translation $((0),(-6))$

a point (x ,y) → (x ,y-6)

hence A'(-8 ,3) → A''(-8 ,-3) and B'(-6 ,4) → B''(-6 ,-2)

Third transformation: Under a reflection in the y-axis

a point (x ,y) → (-x ,y)

hence A''(-8 ,-3) → A'''(8 ,-3) and B''(-6 ,-2) → B'''(6 ,-2)

Thus $(3,8)to(8,-3)" and " (4,6)to(6,-2)$

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A line segment has endpoints at $(3, 8)$ $(3 ,8 )$ and $(4, 6)$ $(4 ,6)$ . If the line segment is rotated about the origin by $\frac{π}{2}$ $(pi )/2$ , translated vertically by $- 6$ $-6$ , 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 (3 ,8 )(3,8)(3 ,8 ) and (4 ,6)(4,6)(4 ,6). If the line segment is rotated about the origin by (pi )/2 π2(pi )/2 , translated vertically by -6 −6-6 , 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 $(3, 8)$ $(3 ,8 )$ and $(4, 6)$ $(4 ,6)$ . If the line segment is rotated about the origin by $\frac{π}{2}$ $(pi )/2$ , translated vertically by $- 6$ $-6$ , and reflected about the y-axis, what will the line segment's new endpoints be?