Answer:
[tex](a)\ (-7,-3)\ \&\ (7,-3)[/tex]
Step-by-step explanation:
Given
Options a, b and c
Required
Points that are reflections across y-axis
The rule of reflection across the y-axis is:
[tex](x,y) \to (-x,y)[/tex]
Testing the given options:
[tex](a)\ (-7,-3)\ \&\ (7,-3)[/tex]
Rule: [tex](x,y) \to (-x,y)[/tex]
[tex](-7,-3) \to (-(-7),-3)[/tex]
[tex](-7,-3) \to (7,-3)[/tex]
This is true, because the actual reflection equals the given reflection
[tex](b)\ (-5,4)\ \&\ (5,-4)[/tex]
Rule: [tex](x,y) \to (-x,y)[/tex]
[tex](-5,4) \to (-(-5),4)[/tex]
[tex](-5,4) \to (5,4)[/tex]
This is not true, because the actual reflection does not equal to the given reflection
[tex](c)\ (1,-8)\ \&\ (1,8)[/tex]
Rule: [tex](x,y) \to (-x,y)[/tex]
[tex](1,-8) \to (-1,-8)[/tex]
This is not true, because the actual reflection does not equal to the given reflection
Hence
[tex](a)\ (-7,-3)\ \&\ (7,-3)[/tex] is a reflection of each other across y axis
