A line segment has endpoints at $(3, 7)$ $(3 ,7 )$ and $(4, 5)$ $(4 ,5)$ . If the line segment is rotated about the origin by $\frac{π}{2}$ $(pi )/2$ , translated vertically by $2$ $2$ , and reflected about the y-axis, what will the line segment's new endpoints be?

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Answer 1 · 2017-07-06T13:13:53

The new endpoints are $= (7, 5)$ $=(7,5)$ and $= (5, 6)$ $=(5,6)$

Let the points be

$A = (3, 7)$ $A=(3,7)$ and $B = (4, 5)$ $B=(4,5)$

The rotation about the origin by $\frac{π}{2}$ $pi/2$ will transform the

$(x, y)$ $(x,y)$ into $(- y, x)$ $(-y,x)$

Therefore,

$A'=(-7,3)$ and $B'=(-5,4)$

The vertical translation will only change the $y$ coordinate

$A''=(-7,5)$ and $B''=(-5,6)$

The reflection in the $y$ axis will change the sign of the $x$ coordinate

$A'''=(7,5)$ and $B'''=(5,6)$

A line segment has endpoints at (3 ,7 )(3,7)(3 ,7 ) and (4 ,5)(4,5)(4 ,5). If the line segment is rotated about the origin by (pi )/2 π2(pi )/2 , translated vertically by 2 22 , and reflected about the y-axis, what will the line segment's new endpoints be?