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Find the image of A (-6, 5) after two reflections, first across the line y = -5, then across the
line x = -12. Write your answer for both reflections or show your graph with each step. (2
points)
a. Reflection 1: y = -5 :
b. Reflection 2: x = -12 :

Respuesta :

kudzordzifrancis

Answer:

a. [tex]A'(-6,-15)[/tex]

b. [tex]A''(-18,-15)[/tex]

Step-by-step explanation:

The given point is [tex]A(-6,5)[/tex].

We want to find the image after this point has been reflected in the line [tex]y=-5[/tex].


Recall that, the mapping for a reflection in the line [tex]y=k[/tex] is


[tex]P(x,y)\rightarrow P'(x,2k-y)[/tex].


This implies that,


[tex]A(-6,5)\rightarrow A'(-6,2(-5)-5)[/tex].


This simplifies to,


[tex]A(-6,5)\rightarrow A'(-6,-10-5)[/tex].


This will finally give us,


[tex]A(-6,5)\rightarrow A'(-6,-15)[/tex].


b. We now apply the second reflection, which is a reflection in the line [tex]x=-12[/tex].


Recall again that, the reflection in the line [tex]x=k[/tex] has the mapping


[tex]P(x,y)\rightarrow P'(2k-x,y)[/tex].


This implies that,

[tex]A'(-6,-15)\rightarrow A''(2(-12)--6,-15)[/tex].

This implies that,

[tex]A'(-6,-15)\rightarrow A''(-24+6,-15)[/tex].


This will finally give us,


[tex]A'(-6,-15)\rightarrow A''(-18,-15)[/tex].


See graph in attachment.






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