Respuesta :
Answer:
The points which are reflections across both axis are;
1) (1.5, -2) and [tex]\left (-1\dfrac{1}{2} , \ 2\right )[/tex]
2) (1.75, -4) and [tex]\left (-1\dfrac{3}{4} , \ 4\right )[/tex]
Step-by-step explanation:
The coordinate of the image of a point after a reflection across the 'x' and 'y' axis are given as follows;
[tex]\begin{array}{ccc}& Preimage&Image\\Reflection \ about \ the \ x-axis&(x, \ y)&(x, \, -y)\\Reflection \ about \ the \ y-axis&(x, \ y)&(-x, \, y)\end{array}[/tex]
Therefore, a reflection across both axis changes (only) the 'x' and 'y' value signs
The given points which are reflections across both axis are;
(1.5, -2) and [tex]\left (-1\dfrac{1}{2} , \ 2\right )[/tex]
We note that [tex]\left (-1\dfrac{1}{2} , \ 2\right )[/tex] = (-1.5, 2)
The reflection of (1.5, -2) across the x-axis gives the image (1.5, 2)
The reflection of the image (1.5, 2) across the y-axis gives the image (-1.5, 2)
Similarly, we have;
(1.75, -4) and [tex]\left (-1\dfrac{3}{4} , \ 4\right )[/tex]
We note that [tex]\left (-1\dfrac{3}{4} , \ 4\right )[/tex] = (-1.75, 4)
The reflection of (1.75, -4) across the x-axis gives the image (1.75, 4)
The reflection of the image (1.75, 4) across the y-axis gives the image (-1.75, 4).
The other points have changes in the values of the 'x' and 'y' between the given pair and are therefore not reflections across both axis
