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

Step2: For question 5

To find the image of reflecting quadrilateral $DLSF$ across the x - axis, change the sign of the y - coordinates of its vertices. Without the actual coordinates or other reference quadrilaterals, we can't name the resulting quadrilateral. But the rule is $(x,y)\to(x, - y)$ for each vertex.

Step3: For question 6

To find the image of reflecting quadrilateral $M'P'T'Z'$ across the y - axis, change the sign of the x - coordinates of its vertices. Without the actual coordinates or other reference quadrilaterals, we can't name the resulting quadrilateral. But the rule is $(x,y)\to(-x,y)$ for each vertex.

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 $x_1=x_2$ and $y_2=-y_1$, it is a reflection across the x - axis. If $y_1 = y_2$ and $x_2=-x_1$, it is a reflection across the y - axis.

Step5: For question 8

Let a vertex of $WHCX$ be $(x_3,y_3)$ and the corresponding vertex of $YBRN$ be $(x_4,y_4)$. Compare the x and y coordinates. If $x_3=x_4$ and $y_4=-y_3$, it is a reflection across the x - axis. If $y_3 = y_4$ and $x_4=-x_3$, it is a reflection across the y - axis.

Step6: For question 9

Let a vertex of $BYNR$ be $(x,y)$ and the corresponding vertex of $PMZT$ be $(x',y')$. Analyze the changes in x and y values. If $x=-x'$ and $y = y'$, it is a reflection across the y - axis; if $x=x'$ and $y=-y'$, it is a reflection across the x - axis.

Step7: For question 10

Let a vertex of $V'K'G'Q'$ be $(x_5,y_5)$ and the corresponding vertex of $HWXC$ be $(x_6,y_6)$. Analyze the relationship between $x_5,x_6,y_5,y_6$. If $x_5=x_6$ and $y_6=-y_5$, it is a reflection across the x - axis. If $y_5 = y_6$ and $x_6=-x_5$, it is a reflection across the y - axis.

Answer:

1. Without specific coordinates or reference, can't name the quadrilateral, but use $(x,y)\to(x, - y)$ for vertices.
2. Without specific coordinates or reference, can't name the quadrilateral, but use $(x,y)\to(-x,y)$ for vertices.
3. Compare x and y - coordinates of corresponding vertices to determine reflection type.
4. Compare x and y - coordinates of corresponding vertices to determine reflection type.
5. Analyze x and y - coordinate changes of corresponding vertices to find reflection rule.
6. Analyze x and y - coordinate changes of corresponding vertices to find reflection rule.