Reflection of the graphics about 2 lines The 2019 Stack Overflow Developer Survey Results Are In Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)The equation of a line reflected about another lineReflection of a curve around a slant lineReflection Of Conic Section About A LineProblem on Straight linesReflection of $x=1$ about $x+y=1$Show if lines $L_1$ and $L_2$ are parallel then reflection $r_L_1L_2$ is a translationFinding the line of reflection and two points of the image with the coordinates of pre-image and one coordinate of imageReflection of line on a sphere.Reflection Matrix and Canonical basisParameterizing lines reflected in a parabola
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Reflection of the graphics about 2 lines
The 2019 Stack Overflow Developer Survey Results Are In
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)The equation of a line reflected about another lineReflection of a curve around a slant lineReflection Of Conic Section About A LineProblem on Straight linesReflection of $x=1$ about $x+y=1$Show if lines $L_1$ and $L_2$ are parallel then reflection $r_L_1L_2$ is a translationFinding the line of reflection and two points of the image with the coordinates of pre-image and one coordinate of imageReflection of line on a sphere.Reflection Matrix and Canonical basisParameterizing lines reflected in a parabola
$begingroup$
$y=sin(x)$ is reflected first in the line $x=y$ and then in the line $y=2$ , what's the equation of the graphics ?
geometry functions graphing-functions
edited Apr 8 at 13:18
Amad
5410
asked Apr 8 at 13:13
QuintisQuintis
6
$endgroup$
|
show 1 more comment
$begingroup$
$y=sin(x)$ is reflected first in the line $x=y$ and then in the line $y=2$ , what's the equation of the graphics ?
geometry functions graphing-functions
edited Apr 8 at 13:18
Amad
5410
asked Apr 8 at 13:13
QuintisQuintis
6
$endgroup$
$begingroup$
What have you tried?
$endgroup$
– Don Thousand
Apr 8 at 13:15
$begingroup$
i used geogebra to solve this however the answer is not correct
$endgroup$
– Quintis
Apr 8 at 13:19
$begingroup$
Why don't you solve it algebraically...
$endgroup$
– Don Thousand
Apr 8 at 13:20
$begingroup$
i could not so please help me to do this
$endgroup$
– Quintis
Apr 8 at 13:22
$begingroup$
Have you learned what a reflection is?
$endgroup$
– Don Thousand
Apr 8 at 13:23
|
show 1 more comment
$begingroup$
$y=sin(x)$ is reflected first in the line $x=y$ and then in the line $y=2$ , what's the equation of the graphics ?
geometry functions graphing-functions
edited Apr 8 at 13:18
Amad
5410
asked Apr 8 at 13:13
QuintisQuintis
6
$endgroup$
$y=sin(x)$ is reflected first in the line $x=y$ and then in the line $y=2$ , what's the equation of the graphics ?
geometry functions graphing-functions
geometry functions graphing-functions
edited Apr 8 at 13:18
Amad
5410
asked Apr 8 at 13:13
QuintisQuintis
6
edited Apr 8 at 13:18
Amad
5410
asked Apr 8 at 13:13
QuintisQuintis
6
edited Apr 8 at 13:18
Amad
5410
edited Apr 8 at 13:18
Amad
5410
edited Apr 8 at 13:18
Amad
5410
5410
asked Apr 8 at 13:13
QuintisQuintis
6
asked Apr 8 at 13:13
QuintisQuintis
6
asked Apr 8 at 13:13
QuintisQuintis
6
6
$begingroup$
What have you tried?
$endgroup$
– Don Thousand
Apr 8 at 13:15
$begingroup$
i used geogebra to solve this however the answer is not correct
$endgroup$
– Quintis
Apr 8 at 13:19
$begingroup$
Why don't you solve it algebraically...
$endgroup$
– Don Thousand
Apr 8 at 13:20
$begingroup$
i could not so please help me to do this
$endgroup$
– Quintis
Apr 8 at 13:22
$begingroup$
Have you learned what a reflection is?
$endgroup$
– Don Thousand
Apr 8 at 13:23
|
show 1 more comment
$begingroup$
What have you tried?
$endgroup$
– Don Thousand
Apr 8 at 13:15
$begingroup$
i used geogebra to solve this however the answer is not correct
$endgroup$
– Quintis
Apr 8 at 13:19
$begingroup$
Why don't you solve it algebraically...
$endgroup$
– Don Thousand
Apr 8 at 13:20
$begingroup$
i could not so please help me to do this
$endgroup$
– Quintis
Apr 8 at 13:22
$begingroup$
Have you learned what a reflection is?
$endgroup$
– Don Thousand
Apr 8 at 13:23
$begingroup$
What have you tried?
$endgroup$
– Don Thousand
Apr 8 at 13:15
$begingroup$
What have you tried?
$endgroup$
– Don Thousand
Apr 8 at 13:15
$begingroup$
i used geogebra to solve this however the answer is not correct
$endgroup$
– Quintis
Apr 8 at 13:19
$begingroup$
i used geogebra to solve this however the answer is not correct
$endgroup$
– Quintis
Apr 8 at 13:19
$begingroup$
Why don't you solve it algebraically...
$endgroup$
– Don Thousand
Apr 8 at 13:20
$begingroup$
Why don't you solve it algebraically...
$endgroup$
– Don Thousand
Apr 8 at 13:20
$begingroup$
i could not so please help me to do this
$endgroup$
– Quintis
Apr 8 at 13:22
$begingroup$
i could not so please help me to do this
$endgroup$
– Quintis
Apr 8 at 13:22
$begingroup$
Have you learned what a reflection is?
$endgroup$
– Don Thousand
Apr 8 at 13:23
$begingroup$
Have you learned what a reflection is?
$endgroup$
– Don Thousand
Apr 8 at 13:23
|
show 1 more comment
1 Answer
1
active
oldest
votes
$begingroup$
The first reflection results in $x=sin y$.
The second one results in $x=sin(4-y)$.
In general the reflection in line $ax+by+c=0$ results in the map:
$$(x,y)mapsto left(fracx(b^2-a^2)-2a(by+c)a^2+b^2,fracy(a^2-b^2)-2b(ax+c)a^2+b^2right)$$
which means:
$$beginalign
a=1,b=-1, c=0:&quad (x,y)mapsto (y,x)\
a=0,b=1,c=-2:&quad (x,y)mapsto (x,4-y)
endalign
$$
answered Apr 8 at 16:55
useruser
6,56011031
$endgroup$
add a comment |
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1 Answer
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active
oldest
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1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
The first reflection results in $x=sin y$.
The second one results in $x=sin(4-y)$.
In general the reflection in line $ax+by+c=0$ results in the map:
$$(x,y)mapsto left(fracx(b^2-a^2)-2a(by+c)a^2+b^2,fracy(a^2-b^2)-2b(ax+c)a^2+b^2right)$$
which means:
$$beginalign
a=1,b=-1, c=0:&quad (x,y)mapsto (y,x)\
a=0,b=1,c=-2:&quad (x,y)mapsto (x,4-y)
endalign
$$
answered Apr 8 at 16:55
useruser
6,56011031
$endgroup$
add a comment |
$begingroup$
The first reflection results in $x=sin y$.
The second one results in $x=sin(4-y)$.
In general the reflection in line $ax+by+c=0$ results in the map:
$$(x,y)mapsto left(fracx(b^2-a^2)-2a(by+c)a^2+b^2,fracy(a^2-b^2)-2b(ax+c)a^2+b^2right)$$
which means:
$$beginalign
a=1,b=-1, c=0:&quad (x,y)mapsto (y,x)\
a=0,b=1,c=-2:&quad (x,y)mapsto (x,4-y)
endalign
$$
answered Apr 8 at 16:55
useruser
6,56011031
$endgroup$
add a comment |
$begingroup$
The first reflection results in $x=sin y$.
The second one results in $x=sin(4-y)$.
In general the reflection in line $ax+by+c=0$ results in the map:
$$(x,y)mapsto left(fracx(b^2-a^2)-2a(by+c)a^2+b^2,fracy(a^2-b^2)-2b(ax+c)a^2+b^2right)$$
which means:
$$beginalign
a=1,b=-1, c=0:&quad (x,y)mapsto (y,x)\
a=0,b=1,c=-2:&quad (x,y)mapsto (x,4-y)
endalign
$$
answered Apr 8 at 16:55
useruser
6,56011031
$endgroup$
The first reflection results in $x=sin y$.
The second one results in $x=sin(4-y)$.
In general the reflection in line $ax+by+c=0$ results in the map:
$$(x,y)mapsto left(fracx(b^2-a^2)-2a(by+c)a^2+b^2,fracy(a^2-b^2)-2b(ax+c)a^2+b^2right)$$
which means:
$$beginalign
a=1,b=-1, c=0:&quad (x,y)mapsto (y,x)\
a=0,b=1,c=-2:&quad (x,y)mapsto (x,4-y)
endalign
$$
answered Apr 8 at 16:55
useruser
6,56011031
answered Apr 8 at 16:55
useruser
6,56011031
answered Apr 8 at 16:55
useruser
6,56011031
answered Apr 8 at 16:55
useruser
6,56011031
6,56011031
add a comment |
add a comment |
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$begingroup$
What have you tried?
$endgroup$
– Don Thousand
Apr 8 at 13:15
$begingroup$
i used geogebra to solve this however the answer is not correct
$endgroup$
– Quintis
Apr 8 at 13:19
$begingroup$
Why don't you solve it algebraically...
$endgroup$
– Don Thousand
Apr 8 at 13:20
$begingroup$
i could not so please help me to do this
$endgroup$
– Quintis
Apr 8 at 13:22
$begingroup$
Have you learned what a reflection is?
$endgroup$
– Don Thousand
Apr 8 at 13:23