Question

1. draw the reflection of quadrilateral mptz across the line y = x. label the reflection as mptz.
2. draw the reflection of quadrilateral vkgq across the line y = -x. label the reflection as vkgq.
3. select all of the quadrilaterals that are reflections of quadrilateral ybrn.

• quadrilateral whcx
• quadrilateral mptz
• quadrilateral kvqg
• quadrilateral sfdl
• quadrilateral mptz
• quadrilateral kvqg

1. the algebraic description of the reflection of quadrilateral bywr, the pre - image, is (x,y)→(-x,y). describe how the coordinates of the vertices of quadrilateral bywr, the pre - image, and the coordinates of the vertices of quadrilateral pmzt, the image, can be used to determine the line of reflection.

Explanation:

Step1: Recall reflection rules

For reflection across the line $y = x$, the transformation rule is $(x,y)\to(y,x)$. To draw the reflection of quadrilateral MPTZ across $y = x$, we take each vertex of MPTZ. Let the vertices of MPTZ be $(x_1,y_1),(x_2,y_2),(x_3,y_3),(x_4,y_4)$. The reflected vertices M',P',T',Z' will have coordinates $(y_1,x_1),(y_2,x_2),(y_3,x_3),(y_4,x_4)$ respectively. Plot the new - vertices and connect them to form M'P'T'Z'.

Step2: Analyze reflection across $y=-x$

The rule for reflection across the line $y=-x$ is $(x,y)\to(-y,-x)$. For the reflection of quadrilateral VKGQ across $y =-x$ to get V'K'G'Q', if the vertices of VKGQ are $(a_1,b_1),(a_2,b_2),(a_3,b_3),(a_4,b_4)$, the reflected vertices will be $(-b_1,-a_1),(-b_2,-a_2),(-b_3,-a_3),(-b_4,-a_4)$. Plot and label them.

Step3: Determine reflections of YBRN

To select the reflections of quadrilateral YBRN, we need to check which of the given quadrilaterals (KVQG, MPTZ, WHCX, SFDL, M'P'T'Z', KV'Q'G') follow the correct transformation rules with respect to YBRN. If the transformation rule for the reflection of YBRN is known (e.g., if it is reflection across a particular line), we apply the rule to the vertices of YBRN and compare with the vertices of the given quadrilaterals.

Step4: Analyze the rule $(x,y)\to(-x,y)$

The transformation $(x,y)\to(-x,y)$ represents a reflection across the y - axis. For quadrilateral BYNR (pre - image) and PMZT (image), if we take the vertices of BYNR with coordinates $(x_i,y_i)$ and the vertices of PMZT with coordinates $(-x_i,y_i)$ for $i = 1,2,3,4$, we can say that the line of reflection is the y - axis. The x - coordinates of the pre - image vertices change their signs while the y - coordinates remain the same.

Answer:

1. To draw the reflection of quadrilateral MPTZ across the line $y = x$: Take each vertex of MPTZ, swap its x and y coordinates to get the reflected vertices M',P',T',Z', and then connect them.
2. To draw the reflection of quadrilateral VKGQ across the line $y=-x$: Take each vertex of VKGQ, change the sign of both its x and y coordinates and swap them (i.e., $(x,y)\to(-y,-x)$) to get V'K'G'Q', and then connect them.
3. To select the reflections of quadrilateral YBRN: Apply the appropriate reflection rules to the vertices of YBRN and compare with the vertices of the given quadrilaterals (KVQG, MPTZ, WHCX, SFDL, M'P'T'Z', KV'Q'G').
4. For the transformation $(x,y)\to(-x,y)$ of quadrilateral BYNR to PMZT, the line of reflection is the y - axis. The x - coordinates of the vertices of BYNR change sign while the y - coordinates remain the same to get the vertices of PMZT.