Question

1. which quadrilateral is the image of reflecting quadrilateral dlsf 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

Reflection across x - axis: $(x,y)\to(x, - y)$. Reflection across y - axis: $(x,y)\to(-x,y)$.

Step2: For question 5

If we reflect a quadrilateral $DLSF$ across the x - axis, we change the sign of the y - coordinates of its vertices. Without the actual coordinates or a visual of the quadrilateral, we can't name the resulting quadrilateral, but the transformation rule for each vertex $(x,y)$ of $DLSF$ to the corresponding vertex of the image is $(x,y)\to(x, - y)$.

Step3: For question 6

If we reflect a quadrilateral $M'P'T'Z'$ across the y - axis, we change the sign of the x - coordinates of its vertices. The transformation rule for each vertex $(x,y)$ of $M'P'T'Z'$ to the corresponding vertex of the image is $(x,y)\to(-x,y)$.

Step4: For question 7

Let a vertex of $BYNR$ be $(x_1,y_1)$ and the corresponding vertex of $FSLD$ be $(x_2,y_2)$. If the reflection is across the x - axis, then $x_1 = x_2$ and $y_2=-y_1$. If across the y - axis, then $x_2=-x_1$ and $y_1 = y_2$. We compare the x and y coordinates of corresponding vertices to determine the axis of reflection.

Step5: For question 8

Similar to question 7, for a vertex $(x_1,y_1)$ of $WHCX$ and corresponding vertex $(x_2,y_2)$ of $YBRN$, we check the relationships between $x_1,x_2,y_1,y_2$. If $x_1 = x_2$ and $y_2=-y_1$, it's a reflection across the x - axis. If $x_2=-x_1$ and $y_1 = y_2$, it's a reflection across the y - axis.

Step6: For question 9

Let a vertex of $BYNR$ be $(x,y)$ and a vertex of $PMZT$ be $(x',y')$. We find the relationship between $x$ and $x'$, $y$ and $y'$. For example, if $x'=-x$ and $y' = y$, it's a reflection across the y - axis. If $x'=x$ and $y'=-y$, it's a reflection across the x - axis.

Step7: For question 10

Let a vertex of $V'K'G'Q'$ be $(x,y)$ and a vertex of $HWXC$ be $(x',y')$. We determine the transformation rule by comparing the x and y coordinates. If $x'=-x$ and $y' = y$, it's a reflection across the y - axis. If $x'=x$ and $y'=-y$, it's a reflection across the x - axis.

Since no coordinates or visual of the quadrilaterals are given, we can't provide the exact named quadrilaterals for questions 5 and 6 or the exact algebraic descriptions for questions 9 and 10. But the general methods are as described above.

Answer:

1. Cannot be determined without more information (use $(x,y)\to(x, - y)$ rule for x - axis reflection).
2. Cannot be determined without more information (use $(x,y)\to(-x,y)$ rule for y - axis reflection).
3. Compare x and y coordinates of corresponding vertices to find axis of reflection.
4. Compare x and y coordinates of corresponding vertices to find axis of reflection.
5. Compare coordinates of corresponding vertices to find the rule (e.g., $(x,y)\to(-x,y)$ or $(x,y)\to(x, - y)$).
6. Compare coordinates of corresponding vertices to find the rule (e.g., $(x,y)\to(-x,y)$ or $(x,y)\to(x, - y)$).