A line segment has endpoints at $(3, 1)$ $(3 , 1)$ and $(2, 3)$ $(2 ,3)$ . If the line segment is rotated about the origin by $π$ $pi$ , translated horizontally by $4$ $4$ , and reflected about the x-axis, what will the line segment's new endpoints be?

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A line segment has endpoints at $(3, 1)$ $(3 , 1)$ and $(2, 3)$ $(2 ,3)$ . If the line segment is rotated about the origin by $π$ $pi$ , translated horizontally by $4$ $4$ , and reflected about the x-axis, what will the line segment's new endpoints be?

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Answer 1 · 2018-01-28T06:37:05

The new endpoints are $(1, 1)$ $(1,1)$ and $(2, 3)$ $(2,3)$ .

Explanation:

Let's apply each of the transformations to both points, one at a time:

$π$ $pi$ rotation around the origin (180º):
$(x, y) \Rightarrow (- x, - y)$ $(x,y)=>(-x,-y)$
$(3, 1) \Rightarrow (- 3, - 1)$ $(3,1)=>(-3,-1)$
$(2, 3) \Rightarrow (- 2, - 3)$ $(2,3)=>(-2,-3)$

Horizontal translation by $4$ $4$ :
$(x, y) \Rightarrow (x + 4, y)$ $(x,y)=>(x+4,y)$
$(- 3, - 1) \Rightarrow (1, - 1)$ $(-3,-1)=>(1,-1)$
$(- 2, - 3) \Rightarrow (2, - 3)$ $(-2,-3)=>(2,-3)$

Reflection over the $x$ $x$ -axis:
$(x, y) \Rightarrow (x, - y)$ $(x,y)=>(x,-y)$
$(1, - 1) \Rightarrow (1, 1)$ $(1,-1)=>(1,1)$
$(2, - 3) \Rightarrow (2, 3)$ $(2,-3)=>(2,3)$

The new endpoints are $(1, 1)$ $(1,1)$ and $(2, 3)$ $(2,3)$ .

Answer 2 · 2018-01-28T10:58:43

$(1, 1) and ((2, 3)$ $(1,1)" and "((2,3)$

Explanation:

$since there are 3 transformations to be performed here$ $"since there are 3 transformations to be performed here"$

$label the endpoints A (3, 1) and B (2, 3)$ $"label the endpoints "A(3,1)" and "B(2,3)$

$First transformation$ $color(blue)"First transformation"$

$under a rotation about the origin by π$ $"under a rotation about the origin by "pi$

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

$rArrA(3,1)toA'(-3,-1)$

$rArrB(2,3)toB'(-2,-3)$

$color(blue)"Second transformation"$

$"under a translation "((4),(0))$

$• " a point "(x,y)to(x+4,y)$

$rArrA'(-3,-1)toA''(1,-1)$

$rArrB'(-2,-3)toB''(2,-3)$

$color(blue)"Third transformation"$

$"under a reflection in the x-axis "$

$• " a point "(x,y)to(x,-y)$

$rArrA''(1,-1)toA'''(1,1)$

$rArrB''(2,-3)toB'''(2,3)$

$"after all 3 transformations"$

$(3,1)to(1,1)" and "(2,3)to(2,3)$

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A line segment has endpoints at $(3, 1)$ $(3 , 1)$ and $(2, 3)$ $(2 ,3)$ . If the line segment is rotated about the origin by $π$ $pi$ , translated horizontally by $4$ $4$ , and reflected about the x-axis, what will the line segment's new endpoints be?

2 Answers

Explanation:

Explanation:

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A line segment has endpoints at (3 , 1)(3,1)(3 , 1) and (2 ,3)(2,3)(2 ,3). If the line segment is rotated about the origin by pi πpi , translated horizontally by 444, and reflected about the x-axis, what will the line segment's new endpoints be?

2 Answers

Explanation:

Explanation:

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A line segment has endpoints at $(3, 1)$ $(3 , 1)$ and $(2, 3)$ $(2 ,3)$ . If the line segment is rotated about the origin by $π$ $pi$ , translated horizontally by $4$ $4$ , and reflected about the x-axis, what will the line segment's new endpoints be?