Question

1. which quadrilateral is the image of reflecting quadrilateral disf across the x - axis?
2. which quadrilateral is the image of reflecting quadrilateral mptz across the y - axis?
3. describe how the coordinates of the vertices of quadrilateral bynr, the preimage, and the coordinates of quadrilateral fsld, the image, can be used to determine the algebraic description of the reflection.
4. describe how the coordinates of the vertices of quadrilateral whcx, the preimage, and the coordinates of quadrilateral ybrn, the image, can be used to determine the algebraic description of the reflection.
5. write the algebraic description for the reflection of quadrilateral bynr, the preimage, onto quadrilateral pmzt, the image.
6. write the algebraic description for the reflection of quadrilateral vkgq, the preimage, onto quadrilateral hwxc, the image.

Explanation:

Step1: Recall reflection rules

When reflecting a point $(x,y)$ across the $x - axis$, the transformation is $(x,y)\to(x, - y)$. When reflecting across the $y - axis$, the transformation is $(x,y)\to(-x,y)$.

Step2: For question 5

To find the image of reflecting quadrilateral $DISF$ across the $x - axis$, we change the sign of the $y$-coordinates of its vertices. Without the actual coordinates of $DISF$ given, we can't name the resulting quadrilateral precisely, but we know the transformation rule for each vertex.

Step3: For question 6

To find the image of reflecting quadrilateral $M'P'T'Z'$ across the $y - axis$, we change the sign of the $x$-coordinates of its vertices. Again, without actual coordinates, we can't name the resulting quadrilateral precisely.

Step4: For questions 7 - 10

Let the vertices of the pre - image quadrilateral be $(x_1,y_1),(x_2,y_2),(x_3,y_3),(x_4,y_4)$ and the vertices of the image quadrilateral be $(x_1',y_1'),(x_2',y_2'),(x_3',y_3'),(x_4',y_4')$.
If we are reflecting across the $x - axis$, we should observe that $x_i=x_i'$ and $y_i'=-y_i$ for $i = 1,2,3,4$. If reflecting across the $y - axis$, we should observe that $x_i'=-x_i$ and $y_i=y_i'$ for $i = 1,2,3,4$. We compare the $x$ and $y$ coordinates of corresponding vertices of the pre - image and image quadrilaterals to determine the axis of reflection and write the algebraic description.

For example, if for all corresponding vertices of the pre - image and image quadrilaterals, the $x$ - coordinates are the same and the $y$ - coordinates have opposite signs, the algebraic description of the reflection is $(x,y)\to(x, - y)$ (reflection across the $x - axis$). If the $y$ - coordinates are the same and the $x$ - coordinates have opposite signs, the algebraic description of the reflection is $(x,y)\to(-x,y)$ (reflection across the $y - axis$).

Since no coordinates are given for the specific quadrilaterals in the questions, we can only provide the general methods as above.

Answer:

1. Cannot be determined without coordinates, use $(x,y)\to(x, - y)$ for each vertex.
2. Cannot be determined without coordinates, use $(x,y)\to(-x,y)$ for each vertex.
3. Compare $x$ and $y$ coordinates of corresponding vertices. If $x$ is same and $y$ has opposite sign, reflection across $x - axis$ with rule $(x,y)\to(x, - y)$. If $y$ is same and $x$ has opposite sign, reflection across $y - axis$ with rule $(x,y)\to(-x,y)$.
4. Compare $x$ and $y$ coordinates of corresponding vertices. If $x$ is same and $y$ has opposite sign, reflection across $x - axis$ with rule $(x,y)\to(x, - y)$. If $y$ is same and $x$ has opposite sign, reflection across $y - axis$ with rule $(x,y)\to(-x,y)$.
5. Cannot be determined without coordinates. Compare $x$ and $y$ coordinates of corresponding vertices to find the rule (either $(x,y)\to(x, - y)$ or $(x,y)\to(-x,y)$ or other more complex reflections if not across axes).
6. Cannot be determined without coordinates. Compare $x$ and $y$ coordinates of corresponding vertices to find the rule (either $(x,y)\to(x, - y)$ or $(x,y)\to(-x,y)$ or other more complex reflections if not across axes).