Given:
The point is A(-1,3).
To find:
The coordinates of the final image. If the given point reflected in
(a) x-axis
(b) line y=4.
Solution:
(a)
If a figure reflected across the x-axis, then
[tex](x,y)\to (x,-y)[/tex]
Using this rule, we get
[tex]A(-1,3)\to A'(-1,-3)[/tex]
Therefore, the coordinates of the final image are A'(-1,-3).
(b)
If a figure reflected across the line y=4, then
[tex](x,y)\to (x,-(y-4)+4)[/tex]
[tex](x,y)\to (x,-y+4+4)[/tex]
[tex](x,y)\to (x,-y+8)[/tex]
Using this rule, we get
[tex]A(-1,3)\to A'(-1,-3+8)[/tex]
[tex]A(-1,3)\to A'(-1,5)[/tex]
Therefore, the coordinates of the final image are A'(-1,5).
