Answer:
The points which are reflections across both axis are;
1) (1.5, -2) and ![\left (-1\dfrac{1}{2} , \ 2\right )](https://tex.z-dn.net/?f=%5Cleft%20%28-1%5Cdfrac%7B1%7D%7B2%7D%20%2C%20%5C%202%5Cright%20%29)
2) (1.75, -4) and ![\left (-1\dfrac{3}{4} , \ 4\right )](https://tex.z-dn.net/?f=%5Cleft%20%28-1%5Cdfrac%7B3%7D%7B4%7D%20%2C%20%5C%204%5Cright%20%29)
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;
![\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}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bccc%7D%26%20Preimage%26Image%5C%5CReflection%20%5C%20about%20%5C%20the%20%5C%20x-axis%26%28x%2C%20%20%5C%20y%29%26%28x%2C%20%5C%2C%20-y%29%5C%5CReflection%20%5C%20about%20%5C%20the%20%5C%20y-axis%26%28x%2C%20%20%5C%20y%29%26%28-x%2C%20%5C%2C%20y%29%5Cend%7Barray%7D)
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 ![\left (-1\dfrac{1}{2} , \ 2\right )](https://tex.z-dn.net/?f=%5Cleft%20%28-1%5Cdfrac%7B1%7D%7B2%7D%20%2C%20%5C%202%5Cright%20%29)
We note that
= (-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 ![\left (-1\dfrac{3}{4} , \ 4\right )](https://tex.z-dn.net/?f=%5Cleft%20%28-1%5Cdfrac%7B3%7D%7B4%7D%20%2C%20%5C%204%5Cright%20%29)
We note that
= (-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